Report
Hydrodynamic Chromatography A chromatographic technique discovered about 13 years ago at The Dow Chemical Company and developed there by a number of scientists now appears to be coming of age. Hydrodynamic chromatography (HDC), as the method is called, is widely used within Dow, and its use should expand as commercial instruments based on it become available in the near future. As with many new instrument developments, HDC was conceived and developed to satisfy a perceived need, in this case the need to reduce the time involved in measuring the size of, and thus better understand and control, colloids. Matter of colloidal dimensions has many forms and impinges in many ways on our daily lives. Clays, viruses, photographic emulsions, paints, and blood are some of the many things that comprise or embody within them this state of matter that in size lies roughly between several nanometers and a few micrometers (Figure 1). The size of such materials is obviously of fundamental interest in our efforts to
understand their behavior or to put them to use. Until recently, however, methods available for size measurement—particularly size distribution analysis— suffered from serious limitations. High cost, complexity of instrumentation, slowness, and often the plain inability to obtain information without compromising the accuracy of the measurement were typical of the difficulties. HDC appears to have overcome many of these limitations. It is fast (recent embodiments of the technique can deliver a complete size distribution in as little as 10 min), the equipment is relatively inexpensive, and, most importantly, since it is in many respects a typically chromatographic technique, it does not call for uncommonly high skill in either obtaining or interpreting data. Though it is fairly conventional from an operating point of view, HDC is from a chromatographic viewpoint quite unusual in at least a couple of ways. In the first place it breaks with one of the often-cited prerequisites for
Polymer Latices Viruses Blood Inorganic Colloids Bacteria
Figure 1 . Particle s i z e r a n g e s 892 A · ANALYTICAL CHEMISTRY, VOL. 54, NO. 8, JULY 1982
successful chromatography, namely, that the species of analytical interest should be soluble in the mobile phase. The "solutes" of HDC are in most cases quite insoluble in the mobile phase. They are in fact in suspension, and at times they are large enough to be seen in a light microscope. Not surprisingly, HDC reveals phenomena and problems not commonly encountered in chromatography. It is in the manner of its separation that HDC is perhaps most unusual and departs radically from conventional practice. Normally chromatography employs two phases—a stationary phase and a mobile phase. The state of the mobile phase, whether it be a gas or a liquid, dictates to which broad class of chromatography a method belongs. Since it employs a liquid as mobile phase, HDC is a branch of liquid chromatography. HDC is unusual, however, in that it does not employ a stationary phase, at least not in the usual sense. Thus the heart of the HDC device is a column packed with spherical particles; but at the same time the interior of these particles is almost invariably quite inaccessible to the "solute" particles being separated. Therefore, any separation that does take place is brought about by phenomena operating exclusively within the void volume of the packed bed. This apparent noninvolvement of a stationary phase has led one author to declare recently (1 ) that HDC is "not truly chromatographic." One of our objectives in this REPORT will be to show how, from a somewhat broader perspective, HDC should be considered chromatographic in nature. But first some background on how the method came about and how it operates. HDC began as a response to a rather specific request. One of us (H.S.) was asked to develop a rapid method 0003-2700/82/0351-892A$01.00/0 © 1982 American Chemical Society
Hamish Small Martin A. Langhorst Dow Chemical USA Midland, Mich. 48640
Figure 2 . B l o c k d i a g r a m of h i g h - s p e e d c o m p u t e r i z e d HDC. R e p r i n t e d w i t h p e r m i s s i o n from J. Colloid Interface Sci.
for determining the size of a commer cial "plastisol" resin whose particles were around 1 μτα in diameter. A method was developed which, though fast, was so narrowly applicable that it brought home the need for some bet ter method of particle size analysis in the submicrometer range.
The idea of extending size-exclusion chromatography to colloids was con sidered but discarded in view of the low diffusivity (D » 10~ 9 cm 2 s _1 ) of the 1-μπι "solute" particles that were of interest at that time. Poor mass transfer of colloid into particles of the requisite porosity would, it was ar
gued, lead to unacceptable peak broadening and poor resolution. As an alternative to size exclusion a mode of separation was proposed that was based on analogies drawn between sorption/desorption of molecularsized species and flocculation/deflocculation of their colloidally dimen sioned counterparts. Accordingly, ex periments got under way wherein short beds of cation exchange resin and a deionized water mobile phase were used in an attempt to separate polystyrene latex particles on the basis of size. Initially the separations obtained were slight and rather un promising. However, most significant was the observation that large parti cles were eluting ahead of smaller par ticles, which was the opposite of what was to be expected if a flocculation/ deflocculation mechanism prevailed. Eventually, with a better under standing of the various interactions involved in transporting colloids through packed beds, it became ap parent that the chromatographic con ditions that were first employed— principally the low ionic strength— did not favor the flocculation mecha nism. In the meantime we set about ex ploring and defining the very inter esting phenomena associated with the particle transport, concurrently devel oping the technique that we later called hydrodynamic chromatography (2). HDC hardware has much in com mon with conventional liquid chroma tography. It employs packed columns and liquid eluents that are usually aqueous solutions of salts and surfac tant. A pump capable of very steady and preferably pulseless delivery at moderate pressures, a sample injection device, a colloid detector (turbidimet er), and various means of data collec tion and processing complete the
ANALYTICAL CHEMISTRY, VOL. 54, NO. 8, JULY 1982 · 893 A
equipment (Figure 2). The column, the heart of the HDC device, is packed with usually spherical particles. A va riety of packing materials have been used—ion exchange resin beads, nonfunctionalized polymer beads, and glass spheres—but the resin has proved to be the best from a practical point of view. The resolving power of the packed columns is critically dependent on the size of the spheres and the manner of their packing. Beads of 15-20 μτη in diameter are commonly used. Early HDC devices used 3-5 m of column (2), but with improvements in packing procedures augmented with comput erized data processing, the perfor mance of columns just 0.5 m long is now adequate for solving a variety of particle size problems. A typical eluent for HDC will con tain a buffer, e.g., sodium phosphate (about 0.01 M) and a surfactant such as sodium lauryl sulfate at about lg/L. Polystyrene latices of very narrow and well-characterized particle size have been extensively employed as model colloids in exploring HDC elution behavior. In a typical experiment a small molecular marker (sodium dichromate) is injected to act as an in ternal monitor of flow variations. Fig ure 3 is a chromatogram from injec tion of a mixture of two monodisperse latices and a simultaneously injected marker. The mixture was eluted through 3 m of 20-μιη cation exchange resin beads in the sodium form. Most noteworthy, of course, is the elution of large particles ahead of the smaller ones, both preceding the marker species. The discovery of this size-sorting ef fect, in addition to pointing the way toward a size analysis method, also
Figure 3. Chromatogram of mixture of two monodisperse latices and dichro mate marker. Reprinted with permis sion from J. Colloid Interface Sci.
provoked a search for a plausible ex planation for the unusual phenome non. It is perhaps appropriate at this stage to take up the question of mech anism and whether HDC can indeed be classified as a chromatographic method. The Basis of H D C
It is customary in HDC to describe particle elution in terms of the Rf number, which is simply the ratio of
the rate of transport of colloid to that of the marker. In most cases the mark er is confined for various reasons to travel in the void space of the column, and its elution rate is therefore a mea sure of the flow rate of the eluent through the packed bed. We have seen how Rf is larger the larger the colloid particle but, in addition, Rf is invari ably greater than unity. In other words, the particles move through the bed with a higher mean velocity than the fluid carrying them. In our initial attempt to explain these unusual observations, we consid ered the crevice region where beads contacted each other as being a sizediscriminating region that admitted species more or less readily depending on their size. However, calculations of this volume for a typical bed showed it to be an insignificant effect in ac counting for the separations observed. A problem in devising a mechanism involved the fact that only a single phase, the eluent, was involved since the beads were quite impermeable to the "solute"—the latex particles. Defi nitions of chromatography, on the other hand, invariably spoke of two phases, one stationary, the other mo bile. But was this two-phase condition a prerequisite for separation? In fact, it is not, and HDC is a good example to illustrate the claim that the prereq uisites for separation are: • relative motion between two contig uous phases or regions of α single phase, and • unequal distribution of solutes be tween these phases or regions of a sin gle phase. Commonly in LC, the condition of relative motion is very obvious—one phase is stationary with respect to the column while the other, the liquid, is not. In HDC the relative motion
Figure 4. (a) Hydrodynamic effect. Colloid particles are excluded from the interface where the fluid velocity is lowest. The larg er the particle is, the greater its mean velocity, (b) Electrostatic effect. Colloid particles are repelled by the charged interface. Thickness (δ) of the excluded zone increases with decreasing ionic strength. Rf increases with decreasing ionic strength 894 A · ANALYTICAL CHEMISTRY, VOL. 54, NO. 8, JULY 1982
cornes about as a result of viscous forces in the flowing eluent that cause it to move more sluggishly the closer it is to the packing-eluent interface. The liquid flow in the interstitial void space is conceptually very similar to the very familiar Poiseuille flow in a capillary, and it is convenient to con sider the complex column void space as a system of such capillaries (Figure 4). When this source of relative flow is coupled with the size-discriminating influence of the interfacial region, which allows more ready access of par ticles the smaller they are, we have satisfied the two prerequisites for sep aration to take place. Techniques such as field flow frac tionation (1 ) also take advantage of unequal flow within a single phase but to obtain the unequal distribution of solutes they must exert an additional influence, namely, the "field." In HDC no such extra influence is required, and in this regard it is more akin to chromatography than is field flow fractionation. If therefore one uses our more broadened concept of the neces sary prerequisites for chromatograph ic separations it is evident that HDC may quite logically be considered a form of chromatography. The early recognition that particle separation was intimately connected with phe nomena of fluid flow prompted the use of the name hydrodynamic chro matography. However, the hydrodynamics of fluid flowing in the column void space and the purely mechanical intrusion of the packing-eluent interface are not the only factors that influence Rf. Since both the packing and colloid have associated double layers, there is a strong electrostatic interaction be tween the two that is in turn greatly influenced by the ionic strength of the eluent. This feature of HDC is amply documented and discussed elsewhere (2), so suffice it to say here that Rf in creases with decreasing ionic strength of the eluent. At sufficiently high ionic strength the dependence of Rf on par ticle size reverses, and large particles have been observed to elute later than smaller ones. This is a manifestation of the influence of van der Waals forces that dominate when electrostat ic repulsion forces become sufficiently suppressed by the ionic environment. It is obvious that the transport of colloidal particles through packed beds is a complex and very intriguing phenomenon, and it is therefore not surprising that much has been done to define and to provide a theoretical basis for HDC elution behavior. For additional background on these mat ters the reader is referred to several original publications (3-5). We devote the remainder of this REPORT to ap plications of HDC.
Particle Size Distribution Though in principle HDC can be applied to a great variety of colloid particle size problems, our examples are of necessity chosen from the area of polymeric latices, since that area is one that has been of most interest and direct concern to us. The calculation of particle size dis tribution is by far the most straight forward application of HDC. In early work, relative particle size distribu tions were obtained by simply com paring chromatograms. In the case of monodisperse samples, the use of this technique afforded a convenient way of determining the size of a colloid. There were problems, however, in applying this approach to polydisperse colloids. In addition, the analysis was slow. To maximize the utility of this technique, the analysis time had to be reduced significantly and some math ematical technique used to calculate the particle size distribution immedi ately following the elution of the chro matogram. Obviously the two keys to this approach were the columns and software. The original columns, constructed of glass packed with either copolymer or cation exchange resin, were several meters long. The columns used today are lk in. o.d., 10 mm i.d. stainless steel tubing, and are less than V2 m long. Typical elution time is less than 6 min. The packing material employed today is lb-μτα cation exchange resin or copolymer. Typically, the measured efficiencies of present HDC columns vary from 27 000-30 000 plates in a 42-cm length of tubing (63 000-70 000 plates/m). These columns have a useful life time of ~ six months of normal use, which corresponds to ~ 2000 samples. Details concerning the preparation and evaluation of these columns can be found elsewhere (6). The successful use of an HDC col umn to measure the particle size dis tribution requires that we characterize the shape of the column band spread ing as closely as possible using some mathematical model. The basic model that we have chosen is a very general one, the Pearson Type VII (7). We have modified this function by addition of an asymmetry factor, which is a linear change in the σ of the peak as a function of direction and distance from the peak center and a "snouting factor," which is an empiri cally derived foretailing, observed with most HDC columns. In the litera ture, the fitting of asymmetrical chro matographic peaks has generally been handled using a convolute integral of a Gaussian peak shape and an exponen tial decay function (8). The linear asymmetry function we have used in our model is much easier to calculate
896 A · ANALYTICAL CHEMISTRY, VOL. 54, NO. 8, JULY 1982
and appears to work as well as the ex ponential decay function for typical HDC peaks. The modified Pearson Type VII distribution can be made to fit most observed HDC peak shapes very accu rately. The algorithm for this model is completely defined by six indepen dent variables. Three variables (loca tion, height, and width) describe the size and location of the peak. Three additional variables (shape factor, asymmetry, and snouting factor) de scribe the shape of the peak. Details concerning this algorithm can be found elsewhere (6). Calculation of Distribution The HDC chromatogram may be written as the convolute integral of several factors with respect to time: F(V) = f[W(t)G(V,t)K(t)]dt
(1)
where: F(V) = observed chromatogram; W(t) = distribution of sample; G(V,t) = band spreading of system; K(t) response of detector; and t = time. F(V) is observed while G(V,t) and Kit) can be measured using monodis perse latex standards. Κ(t), the detec tor response, is actually measured as a function of particle size, but is con verted to a function of time for the calculation. W(t) can then be calculat ed by several numerical techniques. The method we have chosen has been developed empirically and indepen dently for HDC and subsequently found to be very similar to a technique developed for GPC by Ishige, et al. (9). Briefly, the technique involves con volving an assumed distribution with the measured band-spreading func tion and detector response curve to calculate the theoretical chromato gram. The ratio of the height of each point on the measured chromatogram to the corresponding point on the cal culated chromatogram is then used to correct the original distribution esti mate. Other investigators have used math ematical techniques to calculate a par ticle size distribution from an HDC chromatogram (10). While the tech nique that we describe here is similar to that used by Silebi and McHugh, there are differences that are detailed elsewhere (6). Accuracy and Precision A critical question in HDC is whether the particle size distribution calculated from the HDC chromato gram is an accurate representation of the true particle size distribution of the sample. This is difficult to prove when sizing small particles, since the standard method, indeed virtually the
Chromatogram
Computer Deconvolution Using Equation 1
Particle Size Distribution
are obtained when other mixtures of monodisperse latices are analyzed, i.e., the same distributions are calculated individually and in mixtures, even when the chromatographic peaks are almost totally overlapped. It is difficult to define the precision of an entire distribution such as that calculated by HDC. However, the standard deviation of the volume median diameter (50% point on the calculated cumulative volume distribution curve) of a typical 2200 Â polystyrene latex was found to be ±0.85% relative for 15 injections over two days. This precision is typical in HDC and corresponds to an uncertainty in total peak position of ~0.1 s or ±0.03% relative. The absolute accuracy of the amount of material calculated at each diameter has not been rigorously defined for our system. However, HDC has been used to measure the relative amounts of mixtures of 850 Â and 2500 Â monodisperse styrene/butadiene latices. Over a range of 10:90 to 50:50 of the 850:2500 A latices, the absolute error is consistently less than 1%. For example, the mean ratio and standard deviation for 11 consecutive injections of an actual 20:80 ratio mixture is 19.55:80.45 with a standard deviation of 0.73% (6). Particle Aggregation
Figure 5. HDC particle size distribution
only available reference method, transmission electron microscopy (TEM), has inherent errors that may exceed 5-7% for monodisperse latices (11). An indication of the accuracy of HDC may be obtained, however, by comparing the size of a standard latex as determined by T E M and HDC. Such an experiment was conducted in our laboratory in which the volume mean diameter of the standard was reported by T E M to be 2423 Â and by HDC to be 2504 À. The observed error of ~ 3 % relative is less than that inherent in the T E M measurement technique. Our HDC distribution calculation technique has the ability to separate chromatographically unresolved peaks as in Figure 5 into the original monodisperse latices with distributions similar to those obtained when the latices are run individually. Similar results
Interactions between latex particles can bring about their aggregation. Sometimes this is inadvertent and undesirable while at other times the aggregation is intentional and beneficial. HDC has been very effective in elucidating a number of particle aggregation problems. In one case, it was necessary to know if shearing of a particular latex had induced aggregation. Electron microscopic examination of the latex before and after shearing gave an ambiguous result since the sample appeared to be agglomerated before shearing and the apparent agglomeration could have been the result of sample preparation. Chromatograms of the sheared and unsheared latex, however, clearly showed the presence of an extra peak in the former that could be attributed to aggregates (2). The unsheared latex showed no extra peak. In another instance the chromatogram of a supposedly monodisperse latex showed pronounced skewing toward high particle size. Subjecting the dilute latex suspension to an ultrasonic treatment eliminated the skewness and gave a chromatogram that was characteristic of a "monodisperse" latex. We concluded that the latex contained a relatively high concentration of loose aggregates that was effectively broken up by the ultrasonic treatment. These examples illustrate
how in some cases HDC may be very effectively used'to arrive at important qualitative conclusions without resorting to a complete particle size analysis. The measurement of particle association in latex thickener systems is an example of HDC applied to a case where aggregation is intentional and must be controlled. In many latex applications various water-soluble polymers are added to impart desirable rheology to the final product. The development of thixotropic latex paints that are "thick" and dripless on the applicator but free flowing when brushed or rolled is one such example. There is some evidence that this thixotropic behavior is due to a loose bridging of latex particles by the polymeric additives, and HDC offered a possible means of substantiating this. Chromatograms run on unmodified latices and latices to which thickeners had been added clearly showed a shift to faster elution times—presumably larger particles—as more thickener was added. Furthermore, the efficacy of various polymeric thickeners correlated nicely with their effect on the Rf of latices to which they had been added (12). Swelling Effects
HDC has a unique ability to elucidate particle swelling effects in polymer latices. Swelling can be extremely
% Acrylic Acid in S/B/AA Latex
Figure 6. Swelling effects in SBAA latices, indicating the influence of the environment on the effective diameter of the latex particles. Eluent A, pH = 7, sodium lauryl sulfate 0.5 g/L. Eluent B, pH = 10, sodium lauryl sulfate 0.5 g/L. Eluent C, pH = 10, Triton X-100 0.5 g/L. Reprinted with permission from Adv. Colloid Interface Set.
ANALYTICAL CHEMISTRY, VOL. 54, NO. 8, JULY 1982 · 897 A
i m p o r t a n t since it a l t e r s t h e v o l u m e fraction occupied by t h e particles, which in t u r n is a major factor in con trolling rheology. W h e n t h e p o l y m e r p h a s e is of a n o n p o l a r t y p e s u c h as s t y r e n e or s t y r e n e - b u t a d i e n e , t h e vol u m e of t h e particles will n o t b e af fected b y altering t h e p H of t h e a q u e ous p h a s e or its ionic s t r e n g t h or t h e t y p e a n d a m o u n t of s u r f a c t a n t it con t a i n s . On t h e o t h e r h a n d , if t h e latex c o n t a i n s a sufficient level of a n ionic c o m o n o m e r s u c h as acrylic acid, t h e n t h e p a r t i c l e size can be p r o f o u n d l y af fected b y c h a n g e s in t h e s e factors. F i g u r e ' 6 illustrates t h e o b s e r v a t i o n s for a series of s t y r e n e - b u t a d i e n e acrylic acid latices of varying acrylic acid c o n t e n t w h e r e t h e e n v i r o n m e n t was c h a n g e d b y altering t h e p H a n d s u r f a c t a n t in t h e H D C e l u e n t . I t is ev i d e n t how H D C revealed s o m e p r o f o u n d c h a n g e s in t h e size of t h e latex p a r t i c l e s in r e s p o n s e t o t h e c h a n g e s in their aqueous environment. Summary
REAGENTGRADE SOLVENTS Users of Corco chromatographic, elec tronic and spectrophometric reagentgrade solvents know they can count on Corco for highest quality. Reliability. And delivery. In pints, gallons, five-gallons, or drums. At Corco, we've been specialists in reagent-grade solvents since 1953— and have built our reputation on meeting the requirements and specifications of our customers, ACS and ASTM. Corco can also provide reagentgrade acids, bases, and specialty chem icals. Write or call regarding your specific solvent requirements and our complete solvent listing in Bulletin 10. Or circle the number.
CORCO CORCO CHEMICAL CORPORATION Manufacturers of Reagent & Electronic Chemicals Tyburn Road & Cedar Lane · Fairless Hills, Pa. 19030 (215) 295-5006 CIRCLE 32 ON READER SERVICE CARD
S o m e of t h e a t t r i b u t e s of H D C t h a t r e c o m m e n d it as a m e a n s of p a r t i c l e size analysis are: • I t offers a fast, precise m e a n s of analysis in t h e s u b m i c r o m e t e r r a n g e . • I t h a s very b r o a d scope. In a d d i t i o n t o p o l y m e r latices it h a s b e e n u s e d on inorganic colloids such as sil ver halides, silica, ferric oxide, a n d ti t a n i u m oxide, on c a r b o n b l a c k s , a n d on viruses. W h i l e H D C was d e s i g n e d as a tool for colloid s t u d i e s , r e c e n t work h a s d e m o n s t r a t e d its utility in t h e field of very high molecular weight p o l y m e r s for which c o n v e n t i o n a l sizeexclusion c h r o m a t o g r a p h i c m e t h o d s a r e u n s u i t a b l e (13). • T h e e q u i p m e n t is relatively inex pensive a n d if carefully m a i n t a i n e d h a s l o n g - t e r m reliability. • N o special skills h a v e t o be devel o p e d t o p r a c t i c e t h e m e t h o d — i t re q u i r e s only n o r m a l c h r o m a t o g r a p h i c technique. • In m a n y a p p l i c a t i o n s it is n o t necessary t o know o t h e r p r o p e r t i e s of t h e colloid s u c h as refractive index or density. Some other techniques t h a t a r e a p p r o p r i a t e t o t h i s size r a n g e are, on t h e o t h e r h a n d , d e n s i t y as well as size d e p e n d e n t , which c o m p l i c a t e s t h e i r use. • H D C offers a m e a n s of e x a m i n i n g h o w colloids s h r i n k , swell, aggregate, or o t h e r w i s e alter t h e i r effective h y d r o d y n a m i c d i a m e t e r as t h e i r environ m e n t changes. T o our knowledge this is a n ability t h a t is u n i q u e t o H D C . Acknowledgment I n bringing t h i s t e c h n i q u e t o its p r e s e n t s t a t e of d e v e l o p m e n t m a n y Dow scientists h a v e b e e n involved. W e would especially like t o m e n t i o n G. M c G o w a n , R. Pelletier, a n d F . L .
898 A · ANALYTICAL CHEMISTRY, VOL. 54, NO. 8, JULY 1982
S a u n d e r s , w h o h a v e h a d a major p a r t in a p p l y i n g a n d refining t h e t e c h n i q u e . T h e p a t i e n t s u p p o r t of Dow m a n a g e m e n t we also gratefully ac knowledge. T h e H D C m e t h o d d e s c r i b e d in t h i s article is p a t e n t e d b y Dow C h e m i c a l C o m p a n y a n d licensed t o M i c r o m e r i tics I n s t r u m e n t C o r p o r a t i o n for com mercial use. References (1) Giddings, J. C. Anal. Chem. 1981,53, 1170 A. (2) Small, H. J. Colloid Interface Sci. 1974,48,147. (3) Prieve, D. C ; Hoysan, P. M. J. Colloid Interface Sci. 1978, 64, 201. (4) Buffham, B. A. J. Colloid Interface Sci. 1978,67, 154. (5) Silebi, C ; McHugh, A. J. AIChE J. 1978,24(2), 204. (6) McGowan, G. R.; Langhorst, M. A. J. Colloid Interface Sci., in press. (7) Hall, Jr., M. M.; Veeraragharen, V. G.; Rubin, H.; Winchell, P. G. J. Appl. Crystallogr. 1977,10, 66. (8) Grushka, E. Anal. Chem. 1972, 44, 1733. (9) Ishige, T.; Lee, S. I.; Hamielic, A. E. J. Appl. Polym. Sci. 1971,15,1607. (10) Silebi, C. Α.; McHugh, A. J. J. Appl. Polym. Sci. 1979, 23, 1699. (11) Davison, J. Α.; Haller, J. S. J. Colloid Interface Sci. 1974,47, 459. (12) Small, H.; Saunders, F. L.; Sole, J. Adv. Colloid Interface Sci. 1976,6, 237. (13) Prud'homme, R. K.; Froman, G,; Hoagland, D. A. Carbohydr. Res., in press.
Small
Langhorst
Hamish Small, a research scientist with Dow Chemical Company, has a BSc and an MSc from the Queen's University of Belfast, Northern Ire land. He is the inventor of ion chro matography and hydrodynamic chro matography. His research interests include ion exchange (equilibria, ki netics, synthesis, and applications) and liquid chromatography. Martin Langhorst obtained an AB de gree from Centre College (Kentucky) and an MS at the University of Ken tucky. He is a senior research chemist at Dow's Michigan Division Analyti cal Laboratories. His current research interests include chromatographic methods of polymer characterization, membrane separations, hydrodynam ic chromatography, and particle size analysis.
