Methods and apparatus for determining sorption isotherms

A method for determining sorption isotherms of food by inverse chromatography comprising the steps of passing a mobile phase having a known solute concentration and at a known flow rate through a stationary phase comprising a known mass of food at a known temperature, measuring the concentration of solute in the mobile phase leaving the food, determining the amount of solute which has entered the food at selected intervals from the known concentration, known flow rate and time elapsed from the beginning of the passing step, determining the amount of solute which has passed downstream of the food at selected intervals from the measurement of the concentration of the solute, and determining the amount of solute at selected intervals taken up by the food from the difference in the amounts determined above.

FIELD OF THE INVENTION 
This invention relates to a method and apparatus for determining sorption 
isotherms of food. 
BACKGROUND OF THE INVENTION 
Interactions of low molecular weight molecules with food are an integral 
part of food science. Among the most important interactions are those 
involving water with carbohydrates and proteins. This insertion also 
affects food components such as vitamins and enzymes. Equilibrium studies 
in the form of sorption isotherms are particularly useful for evaluating 
the thermodynamics of these interactions. 
A sorption isotherm is essentially a set of data defining the relationship 
at a particular temperature between solute vapor pressure in the 
surroundings and solute content of the food at equilibrium. Most of the 
methods which are used to determine sorption isotherms are gravimetric 
(static methods) and are based upon equilibration of the sample over time 
at constant vapor pressure and temperature. These methods usually require 
long periods of time to achieve equilibrium, and require numerous repeated 
experiments at different vapor pressures to develop the full set of data 
constituting the isotherm. 
Inverse gas chromatography (IGC) has also been used to determine sorption 
isotherms of food. The advantages of using this approach are that small 
samples of materials may be used, sorption data may be determined quickly, 
and the sensitivity of the method in the low vapor pressure region is very 
good. Inverse chromatography is a test method wherein a fluid or "mobile 
phase" bearing the solute is passed through the solid or stationary phase 
material to be studied. The properties of the stationary phase are deduced 
from observations of the solute content in the mobile phase leaving the 
solid. In inverse gas chromatography the mobile phase is a gas. The use of 
specific vapor detectors, such as thermal conductivity, flame ionization 
and mass spectrometry, greatly enhances the specificity and sensitivity of 
the method. 
The inverse gas chromatography method is sensitive to the rate of sorption 
of water vapor and measures kinetic effects which tend to be obscured in 
the long term gravimetric method. Sorption can be controlled in an inverse 
gas chromatography experiment by varying the factors contributing to 
contact efficiency thereby producing insights into the structure of the 
solid phase and into non-equilibrium sorption rate. A study with the 
gravimetric method reveals that this static method may not yield a final 
equilibrium sorption value. Instead, the gravimetric method stops at a 
point where the rate of water vapor sorption to achieve the remaining 
sorption equilibrium differential has slowed down to the point where a 
gravimetric determination shows no measurable gain in weight, a function 
of the sensitivity of the method. 
The two major types of inverse chromatography are frontal analysis and 
pulse (elution) analysis. In frontal inverse chromatography, the entire 
sample of solute is introduced continuously into the column. Frontal 
chromatography may be divided into sorption and desorption phases. When a 
constant supply of mobile phase with a defined single solute concentration 
is supplied to a column, there is an initial delay in transit because of 
solute sorption. This period of delay is followed by a period of 
increasing solute concentration in the stationary phase which produces a 
corresponding rise in solute concentration in the mobile phase leaving the 
column until both phases are saturated in equilibrium with the input 
concentration. Consequently the exit concentration reproduces the sorption 
isotherm for the range of the input partial pressure of the solute. The 
subsequent passage of pure mobile phase produces the desorption isotherm. 
In elution chromatography, an initial concentration of solute is introduced 
into a column of sorbant followed by pure mobile phase. An individual 
component is eluted from the column as a distinct peak as a result of the 
selective retardation of that component by the stationary phase. The peak 
formed on exit has an area proportional to the injected mass and a 
retention time related to the partition coefficient of the equilibrium 
zone. 
The frontal inverse chromatography sorption method provides satisfactory 
agreement with static or long term equilibrium studies but requires a 
series of maintained solute concentrations to cover the full sorption 
isotherm range. The longer equilibrium periods required in frontal inverse 
chromatography, as compared to elution inverse chromatography, also 
require more elaborate controls of the chromatographic conditions. The 
pulse or elution sorption chromatography method, although not as accurate 
as frontal chromatography, has the advantages of rapidity and simplicity. 
The height of the peak in the detector response is related to the partial 
pressure of the solute at any time. The area of the peak is proportional 
to the amount of solute injected, whereas the so-called "pre-peak area", 
and other parameters derived from the detector response versus time, is 
related to the amount sorbed. Since the calculations for the above two 
methods assumes equilibrium conditions, the validity of the methods 
requires ideal conditions, where equilibration is rapid compared to 
transit time. In order to achieve these conditions, the common practice is 
to use low concentrations of solute. Non-linear sorption isotherms, which 
rapidly attain equilibrium in the chromatographic transit time, can also 
be evaluated by inverse chromatography. 
The period of the detector response before elution and after passage of a 
non-sorbed pulse, such as air, is referred to as the prepeak period. The 
area of the detector response during this prepeak period is proportional 
to the sorption at a pressure equivalent to a specific response height 
provided that there are no appreciable non-linear kinetic factors 
restricting elution. The response height is determined by the desorption 
phase. The prepeak time to any specific solute concentration in the gas 
phase is determined by the sorption phase. 
Integrating detector response over the elution concentration profile 
provides prepeak and peak areas proportional to sorption and desorption 
only if there is a linear response of the detector to solute mass, and 
equilibrium is reversible and achieved in solute transit. 
Differences in the proportionality constants between areas and heights for 
mass injected will produce corresponding discrepancies in the calculation 
of sorption isotherms. Such discrepancies result from the existence of 
nonlinear concentration relationships with hysteresis (nonequilibrium 
conditions) for cycles of sorption and desorption. 
In conventional inverse chromatography, only the amount of effluent solute 
leaving the stationary phase is monitored. Incomplete elution of the 
solute from the stationary phase results in underestimation of both 
prepeak and peak area as well as partial solute pressure. The relation 
between height of the peak and vapor pressure, if not linear because of 
incomplete elution of solute, can be seriously in error at low pressure 
when calculated from linear calibration data. These errors tend to 
linearize sorption isotherms that are non-linear when determined by long 
term gravimetric studies. 
The linear transport of a solute in the mobile gas phase isothermally 
through a column containing a stationary phase is characterized by a 
number of changes in the solute concentration created by diverse factors. 
First, there is a partition coefficient between the mobile and stationary 
phases which may vary from a simple concentration independent constant to 
a very complex, concentration dependent constant. Second, the relationship 
can be modified by kinetic effects. These effects include peak broadening 
as a result of solute diffusion in the stationary phase as well as in the 
void volume or carrier gas phase. This broadening is particularly 
significant when solid stationary phases are used as opposed to liquid or 
coated substrates. 
In conventional chromatography, a relatively small mass of solute is 
injected as a sharp pulse into a large mass of solid phase in a long 
column. The pulse rapidly shifts from a sharp square wave shape into a 
Gaussian shape. The peak position and height are governed by thermodynamic 
interactions between the solute and substrate and the peak width is 
governed by diffusional effects. Selection of substrate and solute 
concentration, temperature and flow rate can often be achieved to obtain a 
relatively narrow band maximizing the thermodynamic parameters and 
minimizing diffusional ones. 
One approach to the problem of non-ideal or non-equilibrium conditions is 
to use a post elution pulse of appropriately elevated temperature to elute 
the strongly bound solute as a peak area instead of as a diffuse 
non-quantifiable rear boundary at a lower temperature. Paik, S. W. and 
Gilbert, S. G., Water Sorption Isotherms of Sucrose and Starch by Modified 
Inverse Frontal Gas Chromatography, J. of Chromatogr. 351 (3), 417-423 
(1986). 
Thus, the modified frontal inverse chromatography desorption method 
provides satisfactory agreement with static or long term equilibrium 
studies but requires a series of maintained solute concentrations to cover 
the full sorption isotherm range. The advantages of rapidity and 
simplicity in pulse or elution chromatography method are hence not 
present. 
Accordingly, there have been significant needs for improvements in methods 
and in the apparatus for determining sorption isotherms of food by inverse 
chromatography. 
SUMMARY OF THE INVENTION 
The present invention is directed to a method and an apparatus which 
utilize inverse chromatography to determine sorption isotherms of food. 
One aspect of the present invention provides a method for determining 
sorption isotherms of food systems by inverse chromatography comprising 
the steps of (a) passing a mobile phase having a known solute 
concentration and at a known flow rate through a stationary phase 
comprising a known mass of the food at a known temperature, (b) measuring 
the concentration of the solute in the mobile phase passing downstream of 
the stationary phase, (c) determining the amount of the solute which has 
passed into the mass of the food at selected time intervals during the 
passing step from the known solute concentration, the known flow rate and 
the time elapsed since the beginning of the passing step, (d) determining 
the amount of the solute in the mobile phase which has passed downstream 
from the mass of food at each of said selected time intervals during the 
passing step from the measurements of the concentration of the solute in 
the mobile phase, and (e) determining the amount of solute taken up by the 
food at selected time intervals during the passing step from the 
difference in the amounts determined in steps (c) and (d). 
Another aspect of this invention is directed at an apparatus for 
determining sorption isotherms of food by inverse chromatography. The 
apparatus includes a source of mobile phase, conduit means for conducting 
the flow of the mobile phase towards and away from a chromatograph, an 
injection port for introducing a known amount of a solute into the mobile 
phase, a chromatograph at a known temperature, a pre-column tubing 
disposed in the chromatograph for maintaining the solute pressure in the 
mobile phase at a constant saturated pressure and at a known flow rate, a 
column containing a stationary phase comprising food disposed in the 
chromatograph and a detector measuring means for measuring the amount of 
the solute in the mobile phase passing downstream of the food.

DETAILED DESCRIPTION OF THE INVENTION 
One embodiment of the present invention is illustrated by the apparatus in 
FIG. 1. Helium tank 1 is equipped with a tank valve 2 and a pressure 
regulator valve 3. Valve 3 is adjusted to provide a stream of helium 
carrier gas (mobile phase) at a pressure of about 40 psig in conduit means 
4 (1/8" O.D. copper tubing). Dual flow controller 5 splits the stream of 
carrier gas in conduit means 4 into two streams of carrier gas in conduit 
means 6 and 7. Conduit means 6 and 7 are connected to injection port 9 and 
injection port 10, respectively, each being disposed in injector 8. 
Conduit means 11 connects injection port 9 to pre-column tubing 14 disposed 
in constant temperature bath 13. Pre-column tubing 14 is connected to 
experimental column 16 which in turn is connected to thermal conductivity 
detector 20 through conduit means 18. Similarly, conduit means 12 connects 
injection port 10 to pre-column tubing 15 also disposed in constant 
temperature bath 13. Pre-column tubing 15 is connected to empty column 17 
which in turn is connected to detector 20 through conduit means 19. 
Conduit means 11 and 12 between constant temperature bath 13 and injector 
8 and conduit means 18 and 19 between constant temperature bath 13 and 
thermal conductivity detector 20 are insulated at a level sufficient to 
prevent undue temperature fluctuations. The flow of carrier gas from 
detector 20 is vented through meter 21. The response data from detector 20 
are collected over specific time intervals between samplings and is stored 
on the hard disk of computer 30 using conventional laboratory data logging 
software. 
The temperature of constant temperature bath 13 is maintained by heated and 
cooled water bath 23. The temperature of the heated and cooled water in 
bath 23 is controlled by a conventional thermostat (not shown). Heated and 
cooled water is pumped from bath 23 to constant temperature bath 13 by 
pump 26. Mechanical valves 24 and 25 open and close the supply of heated 
and cooled water to bath 13. Constant temperature bath 13 may be a chamber 
(Hewlett Packard 5750 gas chromatograph) enclosing both experimental 
column 16 and empty column 17. 
The temperature of constant temperature bath 13 may be pulsed by heated 
water bath 22. When the desorption curve has fallen to about 10% of the 
maximum peak height, experimental column 16 and empty column 17 may be 
subjected to a temperature pulse (bake-out condition at 70.degree. C.) to 
remove tightly bound water from the stationary phase in experimental 
column 16. The temperature of the hot water in bath 22 is controlled by a 
conventional thermostat (not shown). Heated water is pumped from bath 22 
to constant temperature bath 13 by pump 29. Mechanical valves 27 and 28 
open and close the supply of heated water to bath 13. 
In a method according to one embodiment of the invention, constant 
temperature bath 13 is maintained at the desired column temperature, 
typically 25.degree., 30.degree., 35.degree. or 40.degree. C. by heated 
and cooled water bath 23. Mechanical valves 24 and 25 are kept open 
whereas valves 27 and 28 are kept closed. Injection 8 is maintained at a 
predetermined vaporization temperature above 100.degree. C. and typically 
about 150.degree.-200.degree. C. The oven surrounding thermal conductivity 
detector 22 is adjusted to a temperature of about 150.degree. C. The 
thermal conductivity detector (TCD) is set at about 150 mA filament 
amperage. The Wheatstone bridge in the thermal conductivity detector is 
balanced. The laboratory data logging software parameters in computer 30 
are set for conditions appropriate for the run. The time interval between 
data points is set at either 1/6 or 1/60 Hz. 
A stream of carrier gas flows from belium tank 1 through conduit means 4 to 
dual flow controller 5. The gas flow rate is adjusted using a soap bubble 
film meter to about 40 cc helium/minute. Dual flow controller 5 splits the 
flow of carrier gas into a first stream and a second stream which flow 
through conduit means 6 and 7, respectively. The first stream of carrier 
gas flows to injector 8 wherein water is introduced into the stream 
through injection port 9. Because the injector 8 is at the relatively high 
vaporization temperature, the water introduced into port 9 vaporizes 
substantially instantaneously. The first stream of carrier gas bearing 
water vapor as a "spike" or bolus then flows from injection port 9 through 
conduit means 11 to pre-column tubing 14 disposed in constant temperature 
bath 13. 
Because pre-column tubing 14 is at the relatively low column temperature 
maintained by bath 13, water vapor in the carrier gas stream condenses on 
the pre-column tubing so that the carrier gas stream flowing downstream 
through the pre-column tubing 14 comes to equilibrium at the column 
temperature. As carrier gas without water flows downstream through 
pre-column tubing 14 after the initial injection, the condensed water 
within the pre-column tubing evaporates, so that the carrier gas flowing 
downstream from the pre-column tubing remains saturated with water vapor 
at the column temperature until the water condensed in the pre-column 
tubing 14 is depleated. 
The first stream of carrier gas flows from pre-column tubing 14 to 
experimental column 16 which contains food material (stationary phase) and 
then through conduit means 18 to thermal conductivity detector 20. The 
response from detector 20 is collected over a specific time intervals 
between samplings and is stored in computer 30. 
In a similar manner, a trace or reference injection may be made for 
external calibration purposes into the empty column of exactly the same 
amount of water to be used in the corresponding run in the experimental 
column and under the same gas chromatographic operating conditions as the 
experimental run. Accordingly, a second stream of carrier gas flows 
through conduit means 7 to injector 8 where solute (water) is introduced 
through injection port 10. The second stream of carrier gas then flows 
from injection port 10 through conduit means 12 to pre-column tubing 15 
disposed in constant temperature bath 13. The second stream of carrier gas 
flows from pre-column tubing 15 to empty column 17 and even through 
conduit means 19 to thermal conductivity detector 20. The response from 
detector 20 is collected over a specific time intervals between samplings 
and is stored in computer 30. 
Constant temperature bath 13 may be subjected to an elevated temperature 
pulse in order to "bake out" columns 16 and 17 and remove tightly bound 
solute. The "bake-out" is accomplished by closing mechanical valves 24 and 
25 from heated and cooled bath 23 and opening mechanical valves 27 and 28 
to heated water bath 22. The water in heated bath 22 is maintained at an 
elevated or "bake-out" temperature of around 70.degree. C. by a 
conventional thermostat. The heated water in bath 22 is pumped by pump 29 
to constant temperature bath 13. This "bake-out" condition is continued 
for 24 hours to remove all residual solute in experimental column 16 
before column 16 is subjected to a second experiment. 
The calibration factor for converting the measurement of the concentration 
of the solute in the mobile phase passing downstream from the mass of the 
food to the amount of the solute in the mobile phase is calculated from 
the corresponding data from the runs using the empty column. Hence, the 
calibration factor or proportionality constant is determined from the 
known amount of solute in the mobile phase entering the empty column and 
the magnitude of the detector response measuring the concentration of 
solute in the mobile phase leaving the column. 
Thereafter, the column bath temperature is stabilized at the desired run 
temperature. Solute is then injected into the experimental column. The run 
is monitored until the peak response has fallen to a level of about 10% of 
the peak height. The column bath temperature is raised from the 
experimental run temperature to the 70.degree. C. "bake out" temperature. 
The run is terminated when the peak response falls to just above the 
baseline noise level and the data is filed on the hard drive. 
The mass of water to be injected into the experimental column and the empty 
column is a predetermined excess quantity of water. The quantity is 
calculated to be at least twice the maximum amount which can be absorbed 
by the mass of the stationary phase when exposed to a water vapor 
saturated stream of carrier gas. With Avicel, a microcrystalline cellulose 
powder with almost no amorphous regions, a mass of water 5 to 10 times the 
maximum amount which the stationary phase can absorb is injected in a few 
injections to yield a prolonged exposure time. With sugar/dextrin 
containing foods, the quantity of water is about equal to the maximum 
amount of water which can be absorbed before sugar liquification occurs. 
Carrier gases useful in the present invention include helium, nitrogen, 
carbon dioxide, oxygen, air and mixtures thereof. The carrier gas is 
maintained at a constant volume flow rate. 
The temperature of the injector should be sufficiently high so as to 
substantially vaporize the predetermined quantity of solute to be injected 
into the port. For water, the temperature of the injector should be in the 
range of from about 150.degree. to about 200.degree. C. 
Solutes useful in the present invention include any solute which may be 
absorbed by a food. These solutes include water, C.sub.3 -C.sub.6 alcohols 
such as 2-propanol and 2-isopropanol, ketones such as acetone and methyl 
ethyl ketone, esters such as methylacetate, C.sub.5 -C.sub.10 hydrocarbons 
such as hexane and aromatics such as toluene. Flavor and aroma components 
may also be used. Water is a preferred solute. 
Foods useful in the present invention include foods which have moisture 
levels in the range of up to about 70%. These foods include but are not 
limited to proteins, carbohydrates, fats, salts and mixtures thereof. 
The temperature of the column should be below the boiling point of the 
solute employed. 
Detectors useful in the present invention include any detector which will 
detect and measure the solute used in the present invention. Preferred 
detectors are thermal conductivity detectors and flame ionization 
detectors. 
The large excess of solute forms a broad band of solute saturated mobile 
phase passing downstream from pre-column tubing 14 to column 16. The term 
"transit width" is used to define the width of such a band. The transit 
width is the time from passage of the leading edge of the band to passage 
of the trailing end, multiplied by the downstream flow velocity. The 
transit width should be significantly greater than the length of the 
column. The combination of a short section of a column containing a 
stationary phase, a low temperature, a low flow rate and a high solute 
mass input relative to solid phase mass saturation, can provide a complete 
sorption isotherm profile ranging from essentially zero to a saturated 
solute partial pressure. 
The post air peak to pre-curve peak area corresponds substantially to 
complete sorption of solute vapor by the stationary phase forming a 
plateau in the response curve. A drop in the maximum peak height is 
attained when the level of solute vapor in the carrier gas stream drops 
from a high (saturated) level to essentially zero. 
The height of the detector response is directly proportional to the solute 
water vapor pressure, thereby providing a linear response in the detector. 
Since the uptake of solute is known, and the vapor pressure of the solute 
is also known at any one time, the kinetic relationship between the solute 
vapor in the mobile phase and the solute vapor in the stationary phase can 
be calculated. 
Quantification of the sorption isotherm is based upon the following 
factors: 
(1) The mass of solute input is a known quantity directly measured by the 
amount injected similar to conventional frontal chromatography where the 
known concentration of solute in carrier gas and known flow rate of 
carrier gas provide a calculated mass of solute. 
(2) The detector response is proportional to the solute partial vapor 
pressure and is determined directly from the constant response plateaus at 
equilibrium of both the experimental column and the empty column. This 
external calibration method avoids the errors inherent in indirect 
calibration methods. 
(3) The mass/area ratio may be determined directly from the known input of 
solute mass and the total area of the peak response. The accuracy of this 
ratio may be determined by injecting pulses of solute into the empty 
column. Errors arising from incomplete elution of solute mass may be 
avoided or measured by determining the difference in response areas of the 
injections of solute into the experimental column and the empty columns. 
Use of high temperature pulse elution aids in the quantification of the 
mass/area ratio even when incomplete elution was present at lower 
temperature. 
The method of the present invention has great utility in gas/solid inverse 
chromatography because of the wide choice of interactions which may be 
studied. The only requirements in gas chromatography are that the 
stationary phase must be nonvolatile and the interacting solute must have 
a finite vapor pressure under the test conditions. 
The method of the present invention also has great utility in liquid/solid 
inverse chromatography. The requirements in liquid chromatograph are that 
the stationary phase must be insoluble in the mobile phase. Ligands can 
also be used to provide a stationary phase when solubility problems exist. 
Vapor uptake and vapor pressure equations were developed which incorporate 
an external calibration factor. This factor may be calculated from runs 
carried out with empty chromatographic columns and is specific only to 
temperature and the solute compound. The empty column external calibration 
provides the proportionality constants for sorption area response to mass 
of solute, and height of response to partial solute vapor pressure. 
Advantages of the present method are the simplicity of the technique 
combined with the accuracy that an external calibration factor offers, 
independent of substrate. By using an excess of solute sufficient to 
saturate both phases, a simple mass balance equation can then be used to 
calculate a sorption isotherm without the need to assume equilibrium is 
attained. Thus the presence of hysteresis error in conventional inverse 
gas chromatography can be avoided. 
The following relations may be utilized: 
##EQU1## 
wherein A.sub.w =water activity, R.sub.h =relative humidity, P.sub.1 
=partial solute pressure at any plateau height response point H.sub.1 in 
the sorption response, H.sub.0 =the plateau height response of empty 
column with P.sub.0 =partial solute pressure for pure solute at the 
specified column temperature in the empty column, and 
##EQU2## 
where M.sub.p1 =mass injected or entering the sorbant by the time=T.sub.1 
(mass input into the column at a time corresponding to H.sub.1), K.sub.a 
=mass/area ratio, Y.sub.1 =area of response defined by the ramp front and 
H.sub.1 at time T.sub.1, A=solute absorbed per unit mass of solid sorbant 
at pressure P.sub.1, and M=mass of solvent or solid phase. 
M.sub.p1 can be calculated from the transit time (or chart distance) 
corresponding to H.sub.1 on the response curve by its ratio to the time 
for total elution, multiplied by the total mass injected or from a 
calibration obtained with an empty column. Thus a plot of mass injected 
versus total elution time gives a coefficient K.sub.t. The product of 
K.sub.t and the time, to any specific point on the response curve, 
provides the mass M.sub.p1 which has come into contact with the solid 
phase during that transit time. A simple procedure and a preferred 
embodiment to calculate the mass absorbed is to determine the difference 
between the total mass input of the solute at any time and the amount of 
solute not absorbed or eluted at that time. For a constant flow rate and 
constant input concentration ratio, as in the modified frontal method, the 
input is given by K.sub.t and the flow time. Unabsorbed or eluted mass is 
given by area Y.sub.1 and the area/mass factor K.sub.a. Thus 
##EQU3## 
These equations may be readily adapted to a data acquisition system based 
on an interfaced microcomputer with appropriate hardware for amplification 
and digitizing of the inverse gas chromatography input. Programs for 
integration and analysis of the data can be used. 
The following example illustrates, but does not limit, certain aspects of 
the present invention: 
EXAMPLE 
Soluble Coffee 
A 4 ounce jar of freeze-dried coffee and an 8 ounce jar of spray-dried 
coffee were passed through a 200 mesh screen. A portion of the spray dried 
coffee was also passed through a 400 mesh screen. 
Corn Starch 
Amioca, a high amylopectin/low amylose corn starch with less than 5% 
amylose content was obtained from the National Corn Starch and Chemical 
Company, Bridgewater, NJ. 
Avicel 
Avicel is a trademark of the FMC Corporation for their microcrystalline 
alpha cellulose. 
Procedure 
A short column, two to five centimeters long, by about 0.6 cm diameter, was 
used at 10% loading of food particulate matter, such as starch granules or 
ground coffee. A typical mass ratio was 100 mg of solid to about 100 ul of 
water, injected at a column temperature of about 25.degree. C. The carrier 
gas flow rate was about 50 ml/min. The thermal conductivity detector 
operated initially at 0.01 millivolt sensitivity. 
Appropriate scan rates, integration and sub-routines were provided to the 
computer to process the chromatographic data into the desired functions 
such as sorption isotherm, cluster function, partition coefficients, etc. 
The data was obtained over a time course which included a preinjection 
period of zeroing the output and a post injection ramp period of 
increasing output response with a constant input concentration until the 
input and output partial pressures were equal. This ramp period was 
defined by the temperature and carrier flow rate and was followed by a 
desorption period of pure carrier gas until at least 90% of the solute 
input mass was exhausted from the solid phase. A post elution temperature 
rise may be used to clear the solid phase of residual solute if it is not 
temperature sensitive. 
The experimental data obtained above with different starches and proteins 
show good agreement between static (weighing) and dynamic (inverse 
chromatography) sorption isotherms. 
As these and other objects, features and advantages of the foregoing 
invention can be utilized without departing from the invention as defined 
in the claims, the foregoing description of the preferred embodiment 
should be taken by way of illustration rather than by way of limitation of 
the invention.