Note: Descriptions are shown in the official language in which they were submitted.
BACKGROUND OF THE INVENTION
The present 'invention relates to a method and
apparatus for determining the amount of a gas adsorbed or
resorbed by a solid in a manner such that the corresponding
adsorption Andre resorption isotherm can bye constructed
from which in turn various morphological characteristics of'
the solid such as surface area, pore size distribution, and
average pore volume, canoe determined.
The measurement of morphological characteristics
of solids, such as catalysts, catalyst supports pigments,
clays, minerals, and composite materializes long been an
outstanding goal of analytical chemistry
For example, a very useful morphological kirk-
touristic of a 'solid Isis surface Aryan' of the most
widely used techniques for surface area determination is that
of gas sorption'. 'Gas sorption techniques-utilize'a theorem-
teal model wherein the surface of the solid it the adsorb
bent) being characterized is viewed as-being covered by a
monolayer of closely packed molecules of an adsorbed gas
(i.e. the adsorb ate). If one can determine the amount
(usually expressed in ml) of adsorb ate in the-monolayer, the
area covered by the monolayer can then easily be calculated
e.g. from the product of the number of molecules' in the
monolayer times the cross sectional area of each molecule. In
193~ Browner, Emmett, and Teller described (J. Am. Chum.
Sock Vol. 60, 2309) a mathematical equation, referred to as
the BET equation, for determining the amount of adsorb ate in
the monolayer from the absorption isotherm of the adsorb ate.
The absorption isotherm is a plot of the amount of the
adsorb ate adsorbed on a solid against either the relative
pressure or the equilibrium pressure of the adsorb ate at a
constant temperature. In order to utilize the BET equation
accurately to determine surface area, one must at least
obtain a sufficient number of data points on the adsorption
isotherm tug be able to determine the point on the adsorption
isotherm at which the "monolayer capacity" occurs. The
"monolayer capacity" is a variable in the BET equation and
--1--
'SOL
--2--
represents the point on the adsorption isotherm wherein a
monolayer of closely packed adsorbed molecules is present at
the surface of the adsorbent. Since the monolayer capacity
generally occurs at an adsorb ate partial pressure of between
about 0.8 and 2.5, one desires to know the adsorption isotherm
at least over this range of partial pressures to be able to
calculate the surface area from the BET equation. It is
significant, however, that while the entire adsorption is-
therm ranging from an adsorb ate partial pressure of 0 to 1
(the adsorb ate partial pressure is one way of expressing the
equilibrium pressure of the adsorb ate as a fraction of the
pressure at which condensation of the adsorb ate occurs under
any set of constant volume and temperature conditions) need
not be known for purposes of determining surface area alone,
the information embodied in the entire adsorption isotherm is
nonetheless very useful for other reasons as described here-
inciter.
Thus, there is a strong incentive to develop anal
lyrical methods which possess the capability of determining
the entire adsorption isotherm.
Adsorption isotherms are conventionally deter-
mined by two general methods, namely, the gravimetric method,
and the volumetric method.
In the gravimetric method the amount of adsorbed
gas at the equilibrium pressure is weighed with the aid of a
micro balance. However, gravimetric methods possess the
disadvantages of limitations in the choice of adsorb ate (e.g.
controlling a sample at liquid nitrogen temperatures is not
feasible); effective temperature control of the sample is
difficult to achieve; and sophisticated and expensive equip-
mint is required to attain the high degree of sensitivity
needed for the measurements. volumetric devices, in contrast,
are simpler and intrinsically more reliable.
In the volumetric method, the volume of the gas
adsorbed is measured rather than the weight. Volumetric
devices conventionally use nitrogen as the adsorb ate at a
temperature of -195C. These devices typically consist of a
--2--
.
I
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gas storage unit and a vacuum source unit connected in
parallel to a volumetric measuring device, referred to as the
dozer unit, of known volume Al; such as a burette or pipette.
The dozer unit can alternately be connected to either the
vacuum unit or the gas storage unit by a series of stopcocks.
The dozer unit in turn is connected in series through another
stopcock to a sample unit, i.e. a chamber of known volume V2
which holds the solid to be tested. By manipulating the
various stopcocks, the dozer and sample units are evacuated,
and the evacuated dozer sealed off from the evacuated sample
chamber. Nitrogen is permitted to slowly enter and fill the
dozer unit from the gas storage -unit at which time the
stopcocks are again manipulated to completely seal of the
dozer while the nitrogen pressure therein i-s measured. When
a constant pressure, Pi, in the dozer is achieved, the
stopcock separating-the sample chamber and:dnser is opened
allowing the- No in the dozer to- expand- into the sample
chamber, the sample chamber and dozer together defining a
third Volume V3 (i.e. Al V2). When the pressure in V3 is
constant, indicative of adsorption equilibrium, it is meat
surged. This equilibrium pricers used to calculate the
total number of moles of No that remains in the was phase. The
number of moles of No adsorbed on the solid is equal to the
moles of No initially present in Volume Al of the dozer plus
the moles of No in the sample chamber defining Volume V2 (the
moles in Volume V2 for the initial run is 0 but increases with
each successive run), less the moles of gaseous No in Volume
V3, after equilibration. The combined data of the amount of
No adsorbed at a particular equilibrium pressure constitutes
a single point on the adsorption isotherm. The above prove-
dune is repeated each time to obtain additional points on the
adsorption isotherm. Each successive run increases the
pressure in the sample chamber until at atmospheric
pressure, saturation of the sample solid with condensed No
occurs, i.e., condensation of No takes place on the sample and
the free space in the sample holder. Conventional practice
is to generate about 8 data points on the absorption isotherm
--3--
'sly
--4--
for surface area determinations. It generally takes one hour
per data point to obtain pressure equilibration. Needless to
say, this method is very time consuming, requiring 2 delays
per data point waiting for equilibration, and the adsorption
isotherm data points are generated on a discontinuous basis.
A detailed summary of this method is provided in the review
paper "The BET Method of Analysis of Gas Adsorption Data and
Its Relevance To The Calculation of Surface Areas" by
Dollimore, D., Sponger, P., and Turner, A., Surface Tech-
neology, Vol. 4, p. 121-160 ~1976).
Discontinuous volumetric gas sorption units have
been improved by automating the opening and closing of the
stopcocks and by increasing the number of sample chambers and
dozer units. the time for equilibration has been shortened
by experimentally determining equilibration times and pro-
tramming the automated system to respond to a preset equip
liberation time. However, this does not alter the disk
continuous nature of unit operations and still requires
excessive waiting time to provide relatively few data points.
Bosch and Peppelenbos describe in the Journal of
Physics E: Scientific Instruments, Vol. 10, p. 605-608
(1977) a dynamic method for determining data points on the
adsorption isotherm. In accordance with this method a
gaseous adsorb ate is introduced into an evacuated sample
chamber of known volume and temperature (e.g. liquid nitrogen
temperature) at what is alleged to be a constant volume flow
rate (e.g., about 1 cm3 SUP Manuel at a partial pressure of
about 0.25) while measuring the pressure. The alleged
constant volume flow rate is achieved by introducing the
adsorb ate into the sample chamber through a capillary tube.
The amount of adsorb ate adsorbed by the adsorbent is cowlick-
fated by comparing the pressure increase in the sample
chamber in the presence of an adsorbing sample against time,
with the pressure increase in a blank (i.e. a sample chamber
having no adsorbing sample present therein) against time. In
the presence of an adsorbent, the adsorb ate gas will be partly
adsorbed and it takes more time to reach a certain pressure
--4--
US
--5--
than it does when using the blank. Thus, the volume of gas
adsorbed by the sample (Via) at a particular pressure is
calculated from the equation:
Eva = TV STOP) to
wherein TV (SUP) is the volume flow through the capillary tube
(cm3 Manuel) at standard temperature and pressure, and t is
the extra time in minutes to reach pressure P compared to a
blank experiment. While the volume flow rate is treated as
being constant for purposes of a single data point on the
adsorption isotherm, it is in fact acknowledged at page 608
that the flow rate is not constant, e.g. when nitrogen is
employed as the adsorb ate, thereby requiring much more labor
riots calculations to generate even a partial adsorption
isotherm. Other disadvantages of this method stem from the
use of a capillary tube to regulate flow. For example, the
characteristics of a fixed capillary tube change with time
and environmental conditions. Thus, fluctuations in ambient
conditions induce fluctuations in the adsorb ate flow rate as
a result of thermoexpansion or contraction of the capillary
tube. Fixed capillaries are not only difficult to menu-
lecture within specified ranges but they are subject to
plugging with solid adsorbent upon resorption and are so
fragile that they need frequent replacement. A mixed leak
capillary cannot be adjusted to control the flow of gas and
provide optimum conditions dictated by the type of adsorbent
sample being employed. More importantly, however, is the
inaccuracy (e.g. 10-15% and higher) introduced into the
adsorption isotherm and surface area determination of very
high surface area materials, e.g. greater than 500 mug if
it is assumed that the volume flow rate is constant. This
stems from the fact that the higher the surface area of the
sample the longer it will take to achieve equilibrium pros-
sure. Consequently, for a given weight of sample, the higher
the surface area, the lower the flow rate must be, and the
lower the flow rate the smaller the I.D. of the capillary tube
must be, thereby enhancing the sensitivity of the flow rate
--5--
ye
6- -
to environmental fluctuations. part from the environ-
mentally induced fluctuations in flow rate as described
above, adsorb ate back pressure, which builds up in the sample
holder as one approaches higher partial pressures in the
adsorption isotherm, also changes? i.e. reduces, the flow
rate. It is admitted in Bosch et at pg. 606 that back pressure
even at a partial pressure of about 0.2 results in a 0.6~
decrease in the flow rate. Such back pressure induced volume
flow fluctuations are magnified as one continues the collect
lion of data points at higher points on the adsorbtionisotherm. Consequently, one is forced to accept increasingly
larger experimental errors over the course of the experiment,
or where possible mathematically compensate for such fluctu-
anions by extremely complicated integration procedures with
respect to the blank and the sample run.
In addition,there;are intrinsic limitations infuse
of a capillary, stemming from the need to maintain the flow rate
ox the adsorb ate to be not greater than the equilibration rate
of adsorption, which prevent attaining a complete adsorption
isotherm from a practical standpoint. For example, in a
capillary system the flow rate is proportional to the pros-
sure drop across the capillary. Consequently, since the
initial flow rate is very low, back pressure reduces the flow
rate even further so that after reaching about 70 to 80% of
the adsorption isotherm, the flow rate becomes almost non-
existent.
Inns, US. Patent No. 2,729,969 discloses a cap-
illary method very similar to Bosch et at. The system
described therein has the same disadvantages discussed above
attributable to the use of a capillary to regulate the flow
of the adsorb ate. Adsorb ate introduction is conducted at a
partial pressure regime of about 0.1 to 0.3 at a flow rate at
about 7 to about 10 cc/min. It is acknowledged at got. 6,
lines 45 et sex, that equilibrium pressure conditions did not
exist at a flow rate of either 10 cumin or 7 cumin when
employing small pore (hence high surface area samples, i.e.
the flow rate was greater than the adsorb ate equilibration
-6-
so
rate of adsorption. However, to obtain lower rates, either
smaller diameter capillary tubes must be employed thereby
increasing the sensitivity of the flow rate to environmental
induced flow rate fluctuations or a lower fore pressure must
be employed thereby increasing the sensitivity of the flow
rate to back pressure induced flow rate fluctuations. At got.
4, lines 5 et sex it is stated that the flow rate is constant
as shown at FIGURE 4 therein. However, FIGURE 4 of this
patent illustrates a flow time of only 150 seconds using only
lo 11 data points. Bosch et at also attempt to support allege-
lions of constant flow rate with a similar plot using a flow
time of 60 minutes and 6 data points. None of this data
illustrate a constant flow rate. over flow times of about 4
his. which are typically needed if the flow rate is to be
maintained below the equilibration rate of adsorption of most
samples of initially unknown surface areas for a time suffix
client to achieve a partial pressure in the monolayer capacity
range, e.g. 0.8-2.5. As stated above, environmental induced
flow rate fluctuations accumulate over extended periods of
time. Consequently, the data used to support allegations of
constant flow rate for the capillary method do not reflect
operating conditions that a commercially successful appear-
tusk would be required to perform under.
Another significant disadvantage of the fixed leak
capillary method develops if one attempts to employ the Bosch
et at capillary system for determining resorption isotherms
(the use of which is discussed hereinafter). In a resorption
experiment, a preadsorbed gas would be removed from the
surface of the sample through the capillary which is con-
netted to a vacuum source. In this procedure the pressure in the sample holder decreases with time. Consequently, the
pressure differential between both ends of the capillary is
reduced over the course of the resorption experiment. Since
this pressure differential is the driving force which removes
the preadsorbed gas from the sample chamber, even a partial
resorption experiment will take between about 20 and about 40
hours to complete. Accordingly, not only is the capillary
icily
-
.
resorption method time consuming but the environmentally
induced volume flow rate fluctuations accumulate over such
extended periods, again necessitating complicated mathemat-
teal corrections to determine the actual volume flow rate
(and therefore the actual amount of gas resorbed at any given
equilibrium pressure) at any given time during the procedure.
Such errors are not discussed in Bosch et air since t-hey art
not concerned with resorption. '`~
Inns does disclose the use of the capillary system'
for resorption. However, apparently because of the problems`
associated with evacuating a chamber through a capillary tube
discussed above, he is forced Tut the nitrogen adsorbed
on the sample at room temperature rather than resorb at liquid
nitrogen temperatures.. Taking the's ample holder ion and out
of liquid nitrogen not only complicates the procedure, but it
introduces significant error in the determination of the
volume of the system which is under equilibrium conditions
at, for example, liquid nitrogen-temperatures. - Such disk
continuity causes the. actual temperature of the sample to
deviate from the liquid nitrogen'temperature'.-~~'1C-varia~ce
in the actual sample temperature relative --to~the:liquid-
nitrogen temperature will invalidate the-test Results.
In summary, neither of the capillary-methods disk
closed by Bosch et at and Inns discloseflow-rates below 1
ml/min at SUP, which are substantially constant as defined
herein for any period of time.
Desorption:isotherms are important because various
mathematical equations are known which enable one to cowlick-
late the pore size distribution of a solid sample from the
data embodied therein. A resorption isotherm is a plot of the
amount of a preadsorbed gaseous material (referred herein as
the desorbate) resorbed from a solid against the equilibrium
pressure of the desorbate at a constant temperature. The
resorption isotherm differs from the adsorption isotherm in
that it is constructed starting with a solid saturated with
the desorbate and gradually reducing the pressure over the
solid to near absolute vacuum. In contrast, the adsorption
-8-
isotherm starts with an evacuated solid sample and increases
the pressure of a gaseous adsorb ate in contact therewith
until sample saturation is reached. The adsorption and
resorption isotherms are collectively known as the sorption
isotherm. Gas-solid interaction can cause at least a portion
of the resorption path of the sorption isotherm to lie higher
on the isotherm plot than the adsorption path. The failure
of the resorption path to duplicate the adsorption path of the
isotherm is commonly referred to as hysteresis. The two most
common forms of hysteresis are referred to as closed loop and
open loop. In the closed loop hysteresis behavior, the
resorption path of the isotherm eventually rejoins the ad
sorption path at some low relative pressure. Closed loop
hysteresis is normally associated with porosity in the sample
being tested. For example, at the start of the:desorption
isotherm, the pores of the sample are saturated and filled
with the desorbate. As resorption occurs, capillary action
delays resorption of the desorbate present within the pores,
such that a lower pressure is required to evacuate the pores
relative to the pressure which initiated the filling of the
pores during adsorption. This delay is expressed as closed
loop hysteresis behavior of the sorption isotherm. Open loop
hysteresis is characterized by the failure of the resorption
path of the isotherm to rejoin with the adsorption path. Open
loop hysteresis is usually associated with some measurable
amount of irreversible adsorption which typically occurs
when the gas reacts with the solid sample upon adsorption,
conventionally referred to as commiseration. Consequently
on resorption, less material will resorb than was initially
adsorbed, giving rise to an open loop in the sorption is-
therm.
By intentionally inducing commiseration much can
be learned about the surface of the solid sample. For
example, commiseration can be employed to determine the %
dispersion and surface area of microscopic particles of a
catalyst deposited on a support by employing a gaseous
adsorb ate which will undergo commiseration with the catalyst
I
~tit,J5~
--10--
particles but not the support.
Other information in the substantially complete
sorption isotherm permits the determination of total pore
volume, average pore size, and pore shape exults vs.
circular pores).
The above discussion highlights only a few of
the incentives for obtaining substantially complete pictures
of the entire sorption isotherm rather than narrow segments
thereof, and any method or device capable of producing
substantially complete sorption isotherms quickly and act
quartile possesses substantial advantages over capillary
methods of the Bosch et at or Inns.
An alternative method for determining adsorption
isotherms has been reported in an article by Nelsen, &
Eggersten, Analytical Chum , vol. 30 p.-13-87 ~1958) titled
"Adsorption Measurements-By A Continuous Flow Method". In
this method, nitrogen is adsorbed by the adsorbent at liquid
nitrogen temperature from a gas stream of nitrogen and
helium, and eluded upon warming the sample. The nitrogen
liberated is measured by thermal conductivity. Thus, the
amount of adsorbed gas-is determined by concentration meat
surmounts in a continuous flow system at atmospheric pressure
rather than by pressure volume measurements at below atoms-
phonic pressure. This method is referred to herein as a
chromatographic method for determining adsorption isotherms
because of its resemblance to chromatography techniques. Two
requirements of this method are steady flow of carrier and
adsorb ate gases, and through mixing of the two gases, in-
situ. In the Nelsen et at method, flow control is provided
by capillary tubes. However in an article by Fancy, and
Tucker, Analytical Chum., Vol. 43, No. 10 p. 1307 (1971)
titled "Determination of Surface Areas By An Improved Con-
tenuous Flow Method", the capillary tubes are replaced with
a series of pressure and mass flow controllers in an attempt
to achieve steady flow (see also, Brat, R., and Irish-
namoorthy, T., Indian Journal of Technology, Vol. 14, p. 170
(1976)). Nitrogen flow rates suitable for the experiment
--10--
I
.
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ranged from 2 to 20 ml/min. however, it is acknowledged at
p. 1309 that flow rates through the detector would moment
tartly change during rapid temperature changes encountered
in the adsorption~desorption cycle. This is not a problem in
the Fancy et at chromatographic method since each data point
is generated on a discontinuous basis over a relatively short
period of time (e.g. 20 min.) and it is within the capably-
flies of the mass flow controller to compensate for these
fluctuations during the production of discontinuous peaks,
i.e. data points. The short duration needed for each peak
also avoids the accumulation of error generated by environ-
mental fluctuations over extended periods of time. In
contrast, the method of the present invention cannot tolerate
even minor uncontrolled fluctuations in the mass flow rate
during the course of the analysis (erg; about 4 his. for
adsorption and 12 his. for desorptionj except as defined
hereinafter. The attainment of this goal in the present
invention is even further complicated by the fact that mast
flow rates in the range of 0.2 to 0~4 ml/min are typically
employed. Such low flow rates are preferred to avoid admix-
sistering or resorbing the gas to the adsorbent or desorbent
respectively at a rate greater than the equilibration rate of
adsorption or resorption, which typically is very low for
high surface area materials- Low flow rates are particularly
troublesome and cannot be achieved by conventional mass flow
controllers at very low pressures where the thermal conduct
tivity of the gases passing there through is very low. This
stems from the fact that conventional mass wow controllers
typically utilize the thermal conductivity of the gas passing
there through as a way of metering the flow of the gas. This
problem is exacerbated by environmental fluctuations in
temperature which cause unwanted, uncontrolled, and accumu-
fated fluctuations in the flow meter sensing elements of
conventional mass flow controllers. Furthermore, the low
thermal conductivity of gases at low pressure and low flow
rates cause the environmentally induced fluctuations in the
flow rate to impart a greater contribution to the total error
--11--
I So
-12-
in the wow rate relative to the use of conventional flow
rates and pressures. Conventional mass flow controllers
therefore are unsuitable for use in practicing the method of
the present invention. Conventional flow meters and thermal
valves which make up the primary components of a conventional
mass flow controller are disarrayed in US. Patent Nosy
3,650,505.; 3,851,526; 3,938,384; and 4,056,975.
In view of-the above, it- i-s evident that there has
been a continuing search for quicker, simpler, and more
accurate methods and apparatus for determining sorption
isotherms. The present invention was developed in response
to this search
Summary of the Invention
- In one asp:e~ct~of~~ë present invention there is
provided a method for determining the amount of a gaseous
adsorb ate adsorbed by a solid absorbent which comprises:
(a) providing an evacuated chamber of known volume
and maintained at a known temperature with an outguessed
sample of adsorbent present therein;
20 - (by introducing gaseous adsorb ate into said sample
containing chamber at a known substantially constant mass
flow rate for a time sufficient to obtain adsorption of at
least a portion of said adsorb ate by said adsorbent, said mass
flow rate being not greater than the equilibration rate of
adsorption of the adsorb ate by the adsorbent and not greater
than about 0.7 ml~min at standard temperature and pressure
conditions;
(c) establishing the equilibrium pressure of said
adsorb ate as it is introduced into said chamber as a function
of time, said equilibrium pressure being the sampled chamber
pressure; and
(d) correlating the adsorb ate sampled chamber pros-
sure, the adsorb ate mass flow rate, and the time needed to
attain said sampled chamber pressure with the amount of
adsorbent adsorbed by the adsorbent at said sampled chamber
pressure.
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US
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In another aspect of the present invention there is
provided a method for determining the amount of desorbate
resorbed as a gas from a solid desorbent saturated with
condensed desorbate which comprises:
(a) providing a chamber of known volume and them-
portray with a previously outguessed sample of desorbent
present therein having said desorbate condensed thereon and
in equilibrium with a chamber atmosphere consisting of gas
eons desorbate; Jo
10(b) withdrawing said desorbate from-said chamber
at a known, substantially constant mass flow rate-which is not
greater than the equilibration rate of resorption, of the
desorbate from the desorbent for a period at least-sufficient
to resorb condensed desorbate from any pores of the sample;
(c) establishing the equilibrium pressure of said
desorbate as it is with-drawn from-said chamber as a-function
of time, said equilibrium pressure being the ~esorbate same
pled chamberJpressure; and
(d) correlating the disrobe simply chamber pros-
Syria, the desorbate mass flow rate, end the-timë needed to
attain said sampled chamber pressure with the amount of
desorbate resorbed at said-sampled chamber pressure.
In still another aspect of the present invention
there is provided an apparatus for determining the amount of
a gas adsorbed by a solid adsorbent sample or resorbed from
a solid desorbent-sample which comprises:
(1) means for defining at least one chamber of
known constant volume to contain said solid sample and a gas
to be introduced into or withdrawn from said chamber means;
30(2) means for continuously introducing a gas into
or withdrawing a gas from said chamber means;
(3) means for establishing the pressure of said gas
as a function of time within said chamber means as it is
introduced or withdrawn therefrom;
(4) means for controlling the mass flow rate of
said gas as it is being introduced or withdrawn from said
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twill
-lo-- .
chamber to be (a) substantially constant over the entire
partial pressure range of gas within said chamber of at least
from about 0.02 to about 1.0, and (b) not greater than the
equilibration rate of adsorption of the gas by the adsorbent
sample during said gas introduction, and not greater than the
equilibration rate of resorption of thetas from the decor-
bent sample during said gas withdrawal; - -
(5) means for evacuating a gas from said-chamber
means and through said control means during withdrawal of
Swede gas from said chamber means; and
(6) means for maintaining a known temperature of
gas within said chamber-to be substantially constant.
Brief Description of the Drawings
.. . . . . . . .. .. . . . .. . .. .
FIGURE 1 is a block diagram of the preferred
component sections of the apparatus of the,present,invention.
FIGURE 2 is a schematic diagram, of the component
parts of each section as depicted in FIGURE l;
FIGURE 3 is a more detailed schematic diagram of
the component parts of the mass flow controller section
present in box 119 of FIGURE 2. . . ..
FIGURE 4 is a more detailed schematic diagram of
the mass flow controller circuit board 401 and flow rug-
feting means within block 403 of FIGURE 3.
FIGURE 5 is a pressure vs. time plot of an ad-
sorption blank calibration run generated in accordance with
Example 1. .. ..
FIGURE 6 is a pressure vs. time plot of adsorption
blank calibration run generated in accordance with Example 2.
FIGURE 7 is a pressure vs. time plot of an ad-
30sorption mode run generated in accordance with Example 3.
FIGURE 8 is a collection of 3 pressure vs. time
plots of a resorption mode run generated in accordance with
Example 4.
FIGURE 9 is a pore size distribution plot generated
in accordance with Example 4.
The diagrammatic showing of FIGURES 2 and 3 omit in
I
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certain instances features which those skilled in the art
would recognize as desirable in actual apparatus operation.
These omissions are made in order to simplify the present-
lion of the invention and to avoid encumbering it with well
understood engineering details. Thus, for example, certain
equipment obviously needed for a power supply, for electrical
connections of solenoid valves, for computer automation,
etc. are omitted from the diagrammatic representation.
Description of Preferred Embodiments
The method of tune present invention-is character-
iced as being dynamic and volumetric. This method can be
conducted in an adsorption-mode,~in a resorption mode, or a
combination of the two wherein the adsorption mode is lot-
lowed by the resorption mode. - ''--
The adsorption move is conducted using a substance
existing initially as a gas-re'ferred'to horns the adsorb
bate, and a solid' referred to herein as the adsorbent or
sample. During the course of the adsorption mode, the
adsorb ate is adsorbed by the adsorbent identity of the
adsorb ate will vary depending on whether the nature of the
adsorption is intended and 'controlled to be physical or
physical and chemical. It is known that adsorption phenomena
Jay be the result of a physical or chemical process depending
on the system involved and 'the temperature employed. Pays-
teal adsorption frequently referred to as van de Weals'
adsorption) is the result of a relatively weak interaction
between solid and gas. One of the characteristics of this
type of adsorption is that all the gas adsorbed by the solid
can be removed therefrom by evacuation at about the same
temperature at which it was adsorbed. Chemical adsorption or
commiseration (during which physical adsorption also takes
place) involves a much stronger interaction between solid and
gas than physical adsorption. A chemically adsorbed gas
cannot be removed from the solid by evacuation at about the
same temperature at which it was adsorbed, and evacuation at
a temperature much higher than the adsorption temperature is
required for the initial removal of chemisorbate. Typically,
; 75 lo
during chemisoeption the adsorbent chemically reacts with the
adsorb ate, Thus, for physical adsorption, the adsorb ate is
selected in conjunction with the adsorbent to be chemically inert
with respect thereto. Furthermore, since the quantity of
physically adsorbed gas at a given pressure increases with
decreasing temperature, the adsorb is typically selected so
that it will liquefy at very low temperatures of typically from
about -195 to about 100C (e.g. -195 to 0C). The adsorbates
employed in the method of the present invention are conventional
in gas sorption volumetric analytical methods.
Representative examples of adsorbates conventionally employed
for physical adsorption include nitrogen, argon, hydrocarbons,
e.g. butane, hexane, Bunsen, H20 and C02.
Representative examples of adsorbates referred Jo herein as
chemi60rbates which are conventionally employed to effect
commiseration include 2~ CO, C02, H20, Ho, and the like-
The identity of the adsorbent or sample can be any solid sought to be analyzed for its morphological characteristics, such
as surface area. The methods described herein are applicable to
samples having a surface area of typically from about 0.01 to
about 1500, preferably from about 0.05 to about 1200, and most
preferably from about 0.5 Jo about 800 mug and pore size radii
of typically from about 5 to about 550, preferably from about 7 to
about 450, and most preferably f Lo about 9 to about 400
angstrom. The above pore size ranges reflect inherent
limitations in the Kelvin equation described hereinafter.
Before determining the amount of adsorb ate adsorbed by a
sample, the sample it cleansed of impurities by removing adsorbed
atmospheric gases (i.e. outguessed) such as nitrogen, oxygen, water
vapor and the like. This achieved by conventional methods as
described in Off, C. and Dallavalle, J. "Fine Particle
Measurement" Macmillan Co., p. 164-204 (1960)
. .
3~2~'75:,l.
--17--
eye r such as for example by heating the sample in a
vacuum at temperatures of about 110 to about 600C ego. 300-
400C) for a period of from about 4 to about 12 his (e.g. 8-
12 his). The sample weight, and optionally density, is also
determined in accordance with conventional methods before
the sample is contacted with the adsorb ate.
The apparatus in which the adsorption mode is
conducted, as described hereinafter in greater detail, come
proses a chamber which can be evacuated. The chamber can be
characterized for purposes of description as comprising two
portions, namely, a sample holder and the lines of the
apparatus which communicate with -the sample holder in an
unrestricted manner during the experiment, through which the
adsorb ate is passed and introduced into the sample holder.
The volume of the chamber is previously and accurately
determined in accordance with conventional volumetric anal
lyrical procedures and t-he ideal was law. This volume is
preferably corrected for the volume of the sample, when
present, based on the density of the sample by subtracting the --
volume of the sample from the volume of the chamber. However when employing a high surface area sample having very small
volume relative to the volume of the chamber, the sample
volume can be ignored as a matter of convenience. When using
the apparatus of the present invention, the sample holder can
be sealed vacuum tight using a stopcock and is removably
detachable from the line portion of the chamber. Thus, as a
matte. of convenience, weighing, outguessing and evacuation
of the sample is normally conducted in the sample holder while
disconnected from the chamber, and the sealed, evacuated
sample holder thereafter connected with the line portion of
the chamber. In accordance with conventional volumetric gas
sorption analytical procedures, the volume of the sample
holder is typically selected to be from about 10 to about 200
times the volume of the sample: to assure an accurate deter-
munition of the reference (blank) for both adsorption and
resorption, to minimize error which can be introduced into
the line volume value at the liquid bath-air interface by
fluctuations it the liquid nitrogen level; and to minimize
error in determining the density of the sample.
The temperature of the adsorb ate is also known and
preferably is constant during the experiment. The temper-
azure of the adsorb ate in the sample holder portion of the
chamber is assumed to be the temperature of the sample holder
portion of the chamber and is typically controlled to ye
within about 1C of the'boiling-point of the adsorb ate at
atmospheric pressure. -Consequently, the temperature of the
chamber sample holder is also determined. This is achieved
by immersing a majority of the sample holder in a liquid bath
of known, preferably constant temperature. -As a matter of
convenience, and to avoid the use-of super atmospheric pros-
sure, the temperature of-the liquid bath is typically surf-
fishnet to cause condensation of'' the adsorb ate' at' about
atmospheric pressure. This is easily achieved by using
liquid adsorbate-at atmospheric pressure as-the''liquid bath
: which controls the temperature of the sample holder, or a
specifically formulated liquid which boils at a temperature
typically not greater than the'~o~ling point of the adsorb ate
at atmospheric pressure. However, in some instances when the
liquid bath is liquefied adsorb ate, impurities within the
liquid bath may cause the bath temperature to be somewhat
higher than the boiling point of the-pure liquefied adsorb
bate. As a result, the saturation pressure of the adsorb ate
(the pressure at which the adsorb ate gas is-in equilibrium
with liquefied adsorb ate) may be above 1 atmosphere. Thy
adsorb ate is said to condense at about atmospheric pressure
in this instance. The sample holder itself typically will
also comprise two portions, namely, a relatively high volume
portion which contains the sample, and a relatively low
volume capillary neck. About half the capillary neck is
immersed in the liquid bath and is considered to be at the
liquid bath temperature, while the remainder of the capillary
neck (which is at room temperature) becomes part of the line
portion of the chamber when connected to the apparatus. The
temperature of the line portion of the chamber is maintained
-18-
~,4t;'l
--19--
.
constant by maintaining about I of the volume (Vc T ) of the
chamber line in a known and constant temperature controlled
environment (e.g. about 39C), so that the adsorb ate within
this volume can be equated to the temperature of the con-
trolled environment and is therefore also constant, Vc T
being the cur line volume at constant temperature in the controller
environment. Pressure readings are then taken of the adsorb
bate in volume Vc T and the temperature of the adsorb ate in
volume Vc T is assumed to be in equilibrium with the adsorb
bate located in the 2% of the chamber line volume which is at
room temperature (OR T Jo Consequently, any fluctuations in
the room temperature are thereby compensated for and disk
regarded. Thus, the temperature differential between the
temperature of Vc T and OR T is sufficiently small, the
volume of Vc T is sufficiently large relative to the total
chamber line volume (Vc T + OR T ), and the total chamber
line volume is sufficiently small relative to the total
chamber volume that this temperature differential is ignored
and the temperature of Vc T is equated to (TO), the butter of
the chamber line volume (AL) of Equations 1 to 3.
- Thus, in this manner an evacuated chamber of
known volume and maintained at a known substantially constant
temperature containing the outguessed sample can be provided.
To this chamber is introduced, preferably continuously, the
adsorb ate at a known substantially constant mass flow rate
preferably for a time sufficient to achieve an adsorb ate
partial pressure of at least OOZE as defined hereinafter, and
most preferably for a time sufficient to condense at least a
portion of the adsorb ate on the adsorbent (i.e. at a partial
pressure of 1) while, establishing the pressure of the
adsorb ate within the chamber as a function of time as it is
so introduced. This pressure is referred to herein as the
sampled chamber pressure.
The term "substantially constant" as applied to
the mass flow rate is defined herein to mean fluctuations, if
any, of not greater than + 0.4~, preferably not greater
than + 0.2~, and most preferably not greater than + 0.15%
-19-
t~7tj~
-20-
in the mass flow rate employed during the entire period of gas
introduction and for substantially the entire prude of gas
withdrawal when Thomas flow rate is not less Ann ml/min;
the phrase "substantially entire period of gas withdrawal"
being defined hereinafter in relation to the partial pressure
range withdrawal is operating within. When the mass flow rate
is between about 0.05 and about 0.19 Mimi the term sub
staunchly constant is defined herein to mean fluctuations,
if any, of no greater than about + I in the mass flow rate.
Mass flow rates below about 0.05 do not have practical utility
since it would take a commercially unacceptable time to
complete a run. The use of a substantially constant mass
flow rate permits one to determine the mass flow rate as
described hereinafter during the entire period during which
the adsorb ate is introduced into the chamber-with an ox-
Tramiel high degree of accuracy not heretofore possible
with conventional methods such as the capillary methods of
Inns and Bosch et at.
The mass flow rate at which the adsorb ate is
introduced into the chamber is selected to be not greater
than the equilibration rate of adsorption of the adsorb ate
by the sample. More specifically, for any given set of
conditions of volume, temperature r pressure, and amount of
adsorb ate in contact with the sample, the rate at which
the molecules of the adsorb ate strike and are adsorbed by
the sample will eventually equal the rate at which the
adsorbed adsorb ate molecules leave the surface of the
simple. When this occurs, the rate of adsorption is no-
feared to herein as the equilibration rate of adsorption.
At conditions of constant volume and temperature,
the establishment of this equilibrium is observed by
constant pressure (i.e. a fluctuation of not greater than
+ 0.25~ of the pressure) of the adsorb ate over a period
OX time, e.g. about 20 to 40 minutes. If the mass flow
rate employed in the present invention is greater than the
equilibration rate of adsorption and administration of the
ad--~rbate is interrupted, it will take a finite period of
-20-
l~t~'7S~L
21-
time until the pressure in the chamber becomes constant. How-
ever, if the mass flow rate it not greater than the equal-
ration rate of adsorption and adsorb ate administration is
interrupted, the pressure will be constant from the time of
interruption. By controlling the mass flow rate to be not
greater than the equilibration rate of adsorption, the pros-
sure established at any given time during-the introduction ox
the adsorb ate, will be the equilibrium pressure. This is
significant because the adsorption isotherm is a plot of the
amount of adsorb ate adsorbed at a given equilibrium pressure.
Consequently, the determination of the adsorption isotherm
is simplified. - -
A mass flow rate capable ox meeting- the above
equilibration rate limitation wilt be proportional to the
weight of the sample. Furthermore, slightly higher mass flow
rates can be employed for lower surface area samples than for
higher surface area samples, since the equilibrium pressure
is more quickly established for the former. In view of the
above, mass flow rates, at standard temperature and pressure
conditions, STOP.) for a sample weight of from about 0.1 to
about 1.0 y, will be not greater than about 0.7, preferably
not greater than about 0.5, and most preferably not greater
than about 0.4 ml/min and typically will vary from about 0.05
to about 0.7 (e.g. 0.05 to 0.19~, preferably from about 0.2
to about 0.5, and most preferably from about 0.2 to about 0.4
ml/min. Since the surface area and porosity of the sample is
often unknown, mass flow rates ox less than 0.5 ml/min,
typically 0.2 to 0.4 ml/min. have been found to be suitable
for most samples. The flow rates described above are char-
acterized as mass flow rates because the mass flow controller described hereinafter, responds to thermal conductivity ox a
gas which is proportional to the mass of the gas. Therefore
milliliters per minute can be converted to mass by thrones
equation.
As stated above, the adsorb ate is preferably in-
traduced into the chamber for a time sufficient to achieve
an adsorb ate partial pressure of at least about 0.20, when
-21-
stowages -
I
the objective is the determination of surface area. How-
ever, when a complete adsorption isotherm is desired an ad-
adsorb ate partial pressure ox at least 0.98 is required. The
partial pressure Pus of the adsorb ate is the chamber
pressure (P) at any given time,e.g.,during adsorb ate intro-
diction, divided by the pressure (Pus) of the adsorb ate
(under the chamber conditions of temperature and volume)
at which liquefaction of the adsorb ate occurs in the
free space of the chamber, i.e. saturation pressure. The partial
pressure is also referred to herein as relative pressure.
At an adsorbatepartial 'pressure above about 0.4, the linear-
fly of the BETTY. plot of equation 5, described hereinafter,
derived from the adsorption isotherm, is gradually lost.
Consequently when the BET equation is to be used to deter-
mine surface area, it is-preferred to utilize the data in ''
the adsorption isotherm between adsorb ate partial pressures
of typically from about-O to about 0.4, preferably from
about 0-to about 0.35,- and most preferably from about 0 to
about 0.30. However, if other mathematical models are
operative to determine surface area at higher adsorb ate
partial pressures in the-adsorption isotherm, this data
also would be usably It's oboe understood that the method
described herein is capable of determining any amount of
adsorb ate adsorption, and the adsorb ate introduction there-
fore must continue for a period at least sufficient to permit
the sample to adsorb at least a portion of the adsorb ate.
As also stated above, the adsorb ate is most pro-
fireball introduced into the chamber for a time sufficient to
condense at least a portion of the adsorb ate on the sample.
Condensation , which is the liquification of the adsorb ate
in the free space of the sample holder, is to be destiny-
gushed from adsorption. Adsorption occurs quickly after
commencement of contact of the sample with the adsorb ate.
Condensation occurs in the presence of a sample as the '
atmosphere in the chamber begins to saturate with the adsorb ate.
Condensation therefore occurs at an adsorb ate partial
-22-
US
.
-23-
pressure (Pups) of 1., Thus, by continuing the adsorb ate
introduction until condensation, a complete adsorption
isotherm can eventually be determined
Accordingly, by achieve sufficient adsorption needed to
attain a monolayer of adsorb ate for surface area determine-
lions the adsorb ate is introduced into the chamber for a
period sufficient Tibetan an adsorb ate partial pressure of
typically greater than about 0.1, preferably grouter than
about 0.2, and must preferably greater than about 0.3
(e.g. greater than about 0.35), and typically will vary
from about 0.2 to about 0'.35, preferably from about 0.25
to about 0.35, and most preferably from about Tao about
0.35. For a complete adsorption isotherm, adsorb ate intro-
diction is continued for a time sufficient to attain a
partial pressure of typically greater than about 0.95, pro-
fireball greater than Abbott and most preferably 1.
Generally at the mass flow rates described herein, but
converted to reflect actual use temperatures and pressures
described herein, such partial pressures reachieved with:
continuous adsorb ate introduction times of typically from
about 2 to about 15, preferably from about 3 to about 12, and
most preferably from about 4 to about 10 his.
- The pressure of the chamber as the adsorb ate is
introduced is established by measuring the adsorb ate
equilibrium pressure as a function of time, erg, starting
from initiation of the adsorb ate introduction. when operate
in at a mass flow rate of not greater than the e~uilibra-
lion rate of adsorption, the sampled chamber pressure will
equal the adsorb ate adsorption equilibrium pressure. The
adsorb ate equilibrium pressure is preferably measured
enough times during the period of adsorb ate introduction
to permit construction of an accurate part of, or complete,
adsorption isotherm. Typically this will involve stab-
fishing from about 100 to aboutlo,ooo, preferably from
about 200 to about 2,000 , and most preferably from about
300 to about 600 pressure data points during adsorb ate
so
introduction. It is even possible to measure the ad-
sorb ate adsorption equilibrium pressure continuously
if desired. However, a frequency of pressure sampling of
about 400 to 600 when operating within an adsorb ate par-
trial pressure range of about 0 to about 0.35 has been
found to be most-efficient for-an adsorption mode BET
surface area determination. . ..
The mass flow rate is not necessarily known
during adsorption of the adsorb~te.by the s-ample but is
determined at some point before or after preferably before,
the sample adsorption run. The most convenient way for
determining the mass flow Ritz. to run a blank wherein
the adsorb ate is introduced into the chamber in--the,ab-
since of a sample,, under the same conditions to be used in
the presence of the sample, while measuring the chamber
equilibrium processor, referred two herein as the reference
pressure, as a function of time. The mass flow rate can
' then be determined at standard temperature and pressure
conditions from the equation,:,, -, . ,. :, .. . .
.. . . . .
MAR = 760 a t (TO- + - (En. 1)
wherein MAR is the mass flow rate for the blank in ml/min;
~P(mnH~) is the chamber pressure change during time in~rval (t),
Vows the chamber line volume (cm3) at temperature TL;VS.H.
is the chamber sample holder volume(cm3~ at temperature
TS.HJ To is the chamber line'temperature~(R)o-f volume AL
and Sly. is the chamber sample holder temperature (OK) of
volume Us H -
Time interval (t) is usually measured from the
start of adsorb ate introduction into the chamber to a time
sufficient to cause the adsorb ate to condense in the chamber.
However, since the pressure/time relationship in a blank
-24-
to Al
-25-
calibration run is linear at a substantially constant flow
rate, time (t) need only be long enough to permit one to
accurately extrapolate the pressure/time plot to the pros-
sure at which adsorb condensation occurs.
Once the mass flow rate is established by the
blank, by using the same mass flow rate to determine the
sampled chamber pressure time relationship, the volume of
adsorb ate adsorbed (Vats) canoe calculated at any it)
during adsorb ate introduction from the following equation:
Vats = 760 ( L ' ( + )
- ' eke. 2)
.. . .
wherein P, AL, TO, ASH ,' and To are as described in-
connection with equation l; pi is the-change in sampled
chamber pressure during the same time interval (t) used to
determine Pus is the-sample holler volume corrected
for the sample volume at temperature TUSH and Tush
temperature of the sample holder having the sample present
therein and of volume OH When using a very low sample
volume relative to the chamber volume, 'thereby permitting
elimination of the correction for the sample volume, and a
time interval starting from the initiation of the adsorb
bate introduction, equation 2 reduces to:
V = 273 (V1 + Vc ) (p - pi) (En. 3)
wherein P is the reference pressure, and P' is the sampled
chamber pressure after time (t) of adsorb ate administration,
the remainder offside varables'being as defined in equation
1. Other mathematical equations can be derived such as
used by Bosch et at wherein the difference in time needed
to attain a particular adsorb ate equilibrium pressure in
the presence and absence of a sample is employed to cowlick-
late the amount, e.g. Volume, of adsorb ate adsorbed by the
.
-25-
7531.
I
sample. In all instances, however, the amount, ego Voyage
is determined by correlating the adsorb ate equilibrium
pressure in the presence of a sample, the mass flow rate,
and the time needed to achieve said adsorb ate equilibrium
pressure.
t is to be noted that during desorption,P is
greater than Put the difference is assigned a positive
value.
The resorption mode is the reverse of the adsorb-
lion mode. The resorption mode employs a solid, referred
to herein as the desorbent or sample, the morphological
characteristics of which are sought to be determined, and
a gas or liquid referred to herein as the-desorbate. The
desorbate is evaporated from the sample during the desorp-
lion mode. Consequently, the resorption mode employs as a
starting material, a sample which is first outguessed as
-described herein and then its surface and any pores present
therein contacted with-an adsorb ate in a manner sufficient
to condense the same on the sample, fill the pores, and
coat the outer surface of the sample with at least-a moo-
layer of condensed desorbate. us a matter of convenience
the sample is typically-saturated with adsorb ate to ensure
complete filling-of the sample pores. Upon condensing the
gas on the sample, it is referred to herein as the-desor-
bate Thus, the term "desorbate" is used in place of
"adsorb ate" merely to identify the mode in which the gas
or liquid constituting the same is employed, and the scope -
of materials which can constitute the adsorb ate and decor-
bate is the same.
Accordingly, to conduct the resorption mode, a
chamber of known, preferably known and constant, volume
and temperature as described in accordance with the adsorb-
lion mode, is provided with a sample having desorbate
condensed thereon and in equilibrium with a chamber atoms-
phone consisting of gaseous desorbate. This typically is
performed by conducting the adsorption mode until sample
-26-
to
-27-
saturation is achieved as described hereinabove. The decor-
bate is then withdrawn, preferably continuously, from the
chamber at a known substantially constant mass flow rate for
a period at least sufficient to resorb condensed desorbate
from the sample, and preferably until complete removal of the
desorbate from the sample. The term "substantially constant"
when applied to the desorbate mass flow rate is defined herein
to apply only at desorbate partial pressures (Pups) of not
less than about 0.02, preferably not less than 0.03, and most
preferably not less than about 0.04. At desorbate partial
pressures of less than about 0.02 the mass flow controller
described herein cannot maintain the mass flow rate sub-
staunchly constant. However, this does not affect the
accuracy of the results-because no usable data is obtained
at a partial pressure range-of 0.02 to 0.
The mass flow rate of desorbate withdrawal is
controlled (in a manner similar to the adsorption flow rate)
to be not greater than the equilibration rate of resorption
of the desorbate from the sample. The equilibration rate of
resorption is the same as defined for the equilibration rate-
of adsorption, with the exception that the equilibrium is
established under conditions of gas withdrawal from, rather
than introduction into, the chamber. The use of these flow
rates simplifies the procedure since the chamber pressure is
the desorbate equilibrium pressure at any given time during
desorbate withdrawal and it is the desorbate equilibrium
pressure which provides data points for axis on the decor-
potion isotherm.
Resorption mass flow rates at a sample weight of
from about 0.05 to about 1.0 g, and at STOP. conditions,
typically will be not greater than about 0.7, preferably not
greater than about 0.5, and most preferably not greater than
about 0.4 ml/min, and typically will vary from about 0.05 to
about 0.7 (e.g., 0.05 to 0.19, and/or 0.2 to 0.7), preferably from about 0.2 to
about 0.4, and most preferably from about 0.2 to about 0.3
ml/min.
slightly higher resorption mass flow rates can be
-27-
-28-
employed for less porous samples relative to samples of
higher porosity, since the equilibration of pressure will
occur more quickly for the former. When the porosity of
the sample is unknown, desorption-mass flow rates of less
than 0.5 ml/min, typically 0.2 to 0.4 ml/min are suitable
for most samples.
As stated above the desorbate withdrawal is
continued for a period at least sufficient to desorb.con-.
dented desorbate from the pores of the sample. In this
regard, the comments distinguishing condensation from
adsorption also apply to the resorption mode., ire complete
resorption of desorbate from the sample surface.tas disk
tinguished from pores-w~thin sample) need not occur, since
the resorption isotherm focuses primarily on the sample
porosity characteristics.- By continuing desorbate with-
drawl until condensed desorbate-is removed from the pores
of the sample, the critical information needed to determine
the pore size distribution is obtained, if one makes a
mathematical correction-for the desorbate which remains
adsorbed on the walls-of the pores. As a matter of con-
lenience it is desirable to remove all desorbate from the
sample.
Resorption from the sample of condensed desorbate
typically will occur at a desorbate partial pressure tops
of less than about 1.0, the desorbate partial pressure being
the same as defined for adsorb ate partial pressure. Accordingly,
the desorbate is withdrawn from the chamber for a time
sufficient to obtain a desorbate partial pressure of typical-
lye less than about 0.20, preferably less than about 0.10,
and most preferably less than about 0.04! and can vary
typically from about 1.0 to about 0.2, preferably from about
1.0 to about 0.1, and most preferably from about 1.0 to about
0.02. Generally at the resorption mass flow rates described
herein converted to reflect actual use temperatures and
pressures, such partial pressures are achieved with con-
tenuous desorbate withdrawal times of typically from about
8 to about 20, preferably from about 8 to about 16, and most
-28-
.. .
issue
I
most preferably from about 9 to about 14 his.
As with the adsorption mode, the chamber pressure
in the presence of a sample, referred to herein as the
resorption sampled chamber pressure, is established as a
function of time during desorbate withdrawal. This is
achieved by measuring the desorbate-equi`li~brium pricers
a function of time., as it is so withdrawn, extorting from.
initiation of desorbate withdrawal. Typicàlly-the desorbate
equilibrium pressure:is~~measured enough times- during the
period of desorhate..withdrawa~ to pe~mit-construction of a
part, preferably all,- ox an accurate deso~p~ion isotherm.
Typically this.will.involve establishing from about 500 to
about 40,000, preferably-frQm about outwit Luke,
and most preferably from about l,000 to about prosier
data points during-desorbate withdrawal Dover the partial
pressure ranges described above. A frequency of pressure
sampling of abuts been found to be suitable for most
samples for typical pore size distribution determinations.
As with the adsorption mode, the resorption mass
flow rate is conveniently determined before or after con-
dueling resorption mode in the presence of the sample, using
a blank. Thus, animate sample holder is saturated with
condensed desorbatë which is then withdrawn at the same
resorption mass flow rate and conditions of temperature and
volume to be used during the resorption mode while measuring
the chamber pressure, referred to herein as the resorption
reference pressure. The resorption mass flow rate can then
be determined in accordance with equation 1 described above.
The pressure/time relationship in the resorption blank
calibration run is linear from a point after removal of
desorbate which has condensed on the sample holder wall down
to a partial pressure of about 0.02. Consequently, the
duration of desorbate withdrawal time (t) in equation 1)
need only be long enough to permit accurate extrapolation of
the blank pressure/time plot to the desorp~ion sampled
chamber pressure at which evaporation of condensed desorbate
-29-
So
~30-
from the pores of the sample occurs, and preferably to the
resorption sampled chamber pressure at which complete
resorption occurs.
Once the resorption mass flow rate is determined,
the use of this same flow rate to determine the resorption
sampled chamber pressure/time relationship permits the
calculation of the volume of desorbate resorbed (Vdsb) at any
time (t) during desorbate withdrawal from equations 2 or 3
described above ~ith-appropriate substitutions by eon-
relating the desorbate equilibrium pressure in the presence of a sample, the resorption mass flow rate, and the time
needed to achieve said desorbate equilibrium pressure
From the Vads-or Vdsb as determined above, the
adsorption isotherm-and/or desorption-isoth'erm can be actor-
mined, e.g.,~for the adsorption isotherm a plot-of voodoos on the
Y axis and the corresponding relative pressu-rè'(P~Ps3 on-the
x-axis UP being the adsorption equilibrium pressure and Pus
being the saturation pressure of the adsorba`te'at toe chamber
temperature) i-s constructed;- while for the-desorptic,n
isotherm, the adsorption equilibrium pressure UP) in the
relative pressure (Pups) is replaced with the corresponding
resorption equilibrium pressure. The information embodied
in the adsorption isotherm can be used to determine the
surface area of the sample by the BETTY. equation; the
information embodied in the resorption isotherm can be used
to determine pore size distribution from the Kelvin equation
and the total pore volume (Up) per gram of sample can be
determined from teetotal volume at SUP of desorbate adsorbed
. .
per gram of sample at saturation pressure Us the molecular
weight of the desorbate (My, the molar volume of the desorbate
(MY), and the density of liquid desorbate (D') in accord-
ante with Equation 11.
The BETTY. equation can be used to determine the
BETTY. surface area of a material. The swept equation
typically is used between relative pressures of 0 to 0.35
for the determination of the internal BETTY. surface area of
a porous material. Roy linearized form of the gut. equation is:
-3G-
t;~';153L
-31-
V(l-Pr) VmC VmC Pry (En. 4)
wherein Pry is the relative pressure (Pups), obtained from
the adsorption isotherm; V is the volume at STOP. of the
adsorb ate adsorbed by the sample per gram of sample at
relative pressure Pry Vim is the monolayer capacity of the
adsorb ate, i.e. the volume of adsorb ate adsorbed as a
monolayer on the sample; end C is the BETTY. constant
dependent on adsorption enthalpy.
Plotting the left hand side of equation 4 versus
Pry should result in a straight line. From the slop and
the Y intercept of this line Vim can be calculated from:
Vim = slope + intercept (En. 5)
, - . . : . -.
The specific BETTY. surface area Sage can
then be calculated from the equation:
BET V N S eke. 6)
V W
earn Vim is as described in equation 4; Nay is Avogadro's
number; Sol is the cross-sectional area of the adsorb ate
20 molecule; Viol is the adsorb ate molar gas volume at STOP.;
and I is the sample weight. ennui it is assumed that the
adsorb ate molecules in the monolayer have the closest
hexagonal packing, the cross-sectional area of an adsorbed
molecule Molly) can be calculated from the following
equation:
2/3
So = 1.091 [i`i/(~a~J)D~ (En. 7)
-31-
I
-32-
wherein M is the molecular weight of the adsorb ate; Nay is
AS described above; and D is the density of the adsorb ate.
The Kelvin equation is used to calculate the
pore size distribution of a porous material. This equation
gives the vapor pressure over a liquid contained in a pore
(or capillary as a function of the pore volume to surface
area per gram ratio of the pore as follows:
do Al 1 ) (En. 8)
.
wherein AL is the molar volume of liquid desorbate at
STOP., AL is the surface tension of the desorbate when in
liquid form; R is the gas constant; T is the absolute
desorbate temperature;~Pr is the desorbate relative pros-
sure; and is the angle of contact between the liquid
desorbate and the pore wall.
If all pores are assumed to be circular and non-
intersecting the following substitution may be made:
. .: .
do 1/2 Ok (En. I
wherein is the Kelvin pore radius of the sample. For fervent
pore systems other substitutions may be necessary as would
be obvious to the skilled artisan. It is assumed the
liquid desorbate in the pores wets the entire surface i.e.
= 0 and COY 0 = 1. This is not unreasonable for desorp-
lion from a porous material. Accordingly, equation 8 may
be written as follows:
lnPr = _ (2) AL ) (En. 10
(I ) (R) (T)
To calculate the pore size distribution, the volt
use of desorbate which is resorbed (vdSb) at a particular
-32-
to
-33- -
pressure interval is determined from the resorption is-
therm. The radius of the pores from which the desorbate
resorbs in that pressure interval can be calculated from the
Kelvin equation after correcting Ok for the amount of decor-
bate which remains adsorbed on the walls of the pores having
a thickness it) from' the equation Rip = Ok + t' wherein t' is
determined from the Halsey equation. Dividing the volume of
desorbate resorbed by the difference in pore radius gives the
frequency in the pore size distribution curve.
A distribution of the pore size vie radius) s
plotted using the value of a Vdsb/~ Rip as the y-axis and the
corresponding value of Rip in angstroms for the x-axis, and the
area under each peak in the plot is integrated to determine
the volume of pores at a particular radius Rip per unit volume
of sample. The corrosion in Ok made for the amount of liquid
desorbate which is adsorbed on the walls of the empty pores
.. . . . . . .
is described by Greg & Sing, "Adsorption Surface Area and
Porosity", NAY. Academic Press, p. 152-165 (1967).
Total pore volume per gram of sample can be de-
.. . .
termined from the equation:
Up = (V~C) My ' - - (En . 11 )
.
the variables of which are described above.
It is to be understood that the present invention
is not limited to any particular mathematical model for using
the information embodied in either the adsorption or de-
sorption isotherm, and such information can be manipulated
as desired in accordance with any conventional procedure.
The method and apparatus of the present invention
can also be employed to effect commiseration. This is useful
because it permits one to determine the surface area and/or
dispersion of very small particles (such as particles which
possess catalytic activity), and referred to herein as the
chemisorbent or active phase, which have been deposited on
larger particle (such as a catalyst support) and referred to
'herein as the support solid.
The dispersion of the active phase can be very
usual in catalyst evaluations because it provides inure-
-33-
SWAHILI
motion about the number of catalytic sites available at the
surface of the support. This area of analytical chemistry it well
developed and the appropriate selection of a suitable
chemisorbate, and the adsorption temperature, for use with a
particular active phase is reviewed fox example in Mutter, J. Rev.
Pure Apply Chum., vol. 19, p. 151 (1969) Fort, R., Ache
Swamp. Series, vol. 143, pp. 143, 70, 9-22 (1970). Active phases
which can be effectively determined with the commiseration method
include Pi, Pod, Nix Co, Cut A and Fe, as well as a variety of
metal oxides including Cry 03, Cut, No, sulfides, and the
like. For example a suitable chemisorbate for a platinum catalyst
is hydrogen which it reactive with platinum at temperatures of
greater than about 0C. Consequently the chemisorp~ion sample
holder temperature it controlled to be at least such temperature.
Accordingly, the chemisoLption mode it conducted by selecting
a suitable chemisorbate in conjunction with the active phase which
will be present on the solid support, such that the chemisorbate
will selectively chemisorb on the surface of the active phase but
not the solid support. The weight percent of active phase
deposited on the spot should be known if the dispe~6ion of the
active phase it sought to be determined. The adsorption mode it
conducted as described herein using a chemisorbate as the
adsorb ate and solid supported active phase as the sample. The
chamber temperature is conventionally selected in conjunction with
the chemisorbate-active phase reactive thresholds to assure
commiseration. Upon completion of the adsorption run, the total
amount of chemi~orbate physically and chemically adsorbed as a
function of time is determined. During this adsorption run, the
chemisorbate will not only be physically adsorbed but will also be
irreversibly chemisocbed by the active phase to the extent that
when the chamber is subsequently evacuated the chemisorbate will
not resorb from the surface of the active phase. In contrast, the
comma-
- 34 -
..... .
'75:;~
35-
sorb ate is only physically adsorbed by the support solid, and
complete resorption of the chemisorbate from the solid
support will occur upon said subsequent evacuation.
Moreover, commiseration by the active phase in the
first adsorption run, will effectively inactivate the no-
active sites of the active phase such that the active
phase will become chemically inert with respect to further
contact with the chemisorbate subsequent to said evacuation.
Upon completion of the initial adsorption run, the
chamber typically is quickly evacuated to resorb the desorbable
chemisorbate. Pressure measurements need not be taken during
evacuation and the rate of evacuation is selected to be as
fast as possible to save time. Upon completion of the
.
evacuation, the adsorption mode is repeated, preferably
immediately, for a second time typically at the same chamber
temperature and mass flow rate employed for the initial
adsorption run, and using the same chemisorbate. During the
second adsorption run, however, only physical adsorption by
the sample will occur, thereby resulting in the adsorption of
less chemisorbate than occurred in the initial adsorption
run. This amount is determined as a function of time, and the
difference in the amount of chemisorbate adsorbed in the
initial and second adsorption runs is determined over the
simpered of time. This difference is the amount of
chemisorbate chemisorbed by the active phase.
- The % dispersion of the active phase on the solid
support can then be determined from the following equation:
% Active Phase Dispersion = B x 100
wherein A is the number of atoms of cnemisorbate chemisorbed
by the active phase, and B is the number of atoms of active
phase on the support solid. The value of A is determined from
the differential amount described above and B is determined
from the weight % of active phase on the support solid. In
addition to the % active phase dispersion, the surface area
of the active phase can also be determined by converting the amount
of chemisorbate irreversibly sorbed tote corresponding number
-35-
-36-
of molecules (atoms) of chemisorbate. The total surface area
of the active phase is then determined from the known no-
lationship between the number of chemisorbate molecules
(atoms) chemisorbed per metal atom of the active phase and the
area of each active phase metal atom.
The preferred embodiment of the apparatus used
to conduct the methods of the present.inven~ion is desk
cried in connection with reference to the figures.
Figure is block diagram of the preferred
components of the Apparatus,. namely gas supply section
to serve as a source of the adsorb ate or desorbate; a
vacuum section capable of evacuating the chamber to a
pressure of not greater. than 10-5, .-preferably not greater
than 10-7, and most preferably not greater than 10-Y mmHg;a
flow controller section which contains a mass flow con-
troller capable.of.controlling: the masts flow rate of the
gas being adsorbed or.desorbed at a substantially constant
value as described herein at the adsorb ate and desorbate
partial pressures also described herein; a pressure sensing
and recording section capable of measuring and recording
the pressure of the adsorb ate or deso-rbate, typically with
an accuracy of within about 0.05 mmH~ of the true pros-
sure value; an adsorption or resorption section which
includes a chamber capable of permitting introduction
and withdrawal of the sample and the adsorb ate or desorbate
into or from a sample holder r as well as permitting control
of the volume and temperature thereof as described herein;
and an outguessing section which employs the vacuum section
to assist in outguessing of the sample.
FIGURE 2 illustrates the component parts of each
section of the apparatus in a schematic diagram. More
specifically, the gas supply section typically will con-
lain one or more gas cylinders 101-104 which contain various
different gases for adsorption or commiseration. Each gas
cylinder is connected to line 211 by conventional vacuum
solenoid valves (ASCOT) 7-10 respectively. These valves
-36-
I
-37-
preferably are actuated in response to a signal from come
putter 117 at the appropriate time to permit gas to enter
line 211. Line 211 is connected to the mass flow con
troller section via lines 200 and 201 through vacuum solenoid
valve 3. During introduction of the gas into sample holder
109~ vacuum selenoid--valve 6 is closed and gas is passed
from line 211 through open valve 3, through lines 200 and
201 and into the mass flow controller section.
The mass flow~controiler section of the apparatus
contains a mass flow controller. A mass flow controller
is an electronic device which operates on an adjustable
aperture principle. The mass flow controller is preset
to deliver gas to line 202 at a particular and sub Stan-
tidally constant mass flow rate, e.g. the flow rate employed
in the blank calibration run. However, due to the fact
that gas passing through the mass flow controller is either
being introduced or withdrawn from sample holder 109, a
back pressure (during adsorption) or back vacuum touring
desertion develops in the sample holder which causes a
decrease in the mass flow rate relative to the preset
value. The mass flow controller continuously senses the
actual flow rate with a flow meter, compares it to the
preset value and compensates for any deviation from the
preset valve by opening or closing the aperture to in-
crease or decrease the flow rate until the preset flow
rate is again established.
In addition to fluctuations in the flow rate
caused by variations in the pressure within the sample
holder, there are other factors which must be controlled
to achieve a substantially constant mass flow rate as
described herein.
or employ, to successfully employ a mass flow
controller for the adsorption and commiseration modes, the
supply of the gas to the flow controller should be maintained
at a substantially constant pressure, since mass flow con-
trollers have been found to correct relative slowly for
. -38-
changes or fluctuations in the incoming gas pressure. By
substantially constant pressure is defined herein to mean
deviations, if any, in the pressure of the incoming gas tooth
mass flow controller of typically not greater than about +
0.35, preferably not greater than about + 0.30, and most
preferably not greater than about + 0.20 psi. Pressure
fluctuations are further reduced with the use of narrow
tubing in the manifold as described herein. For the adsorb-
lion mode, the pressure of the adsorb ate fed Tut mass flow
controller is typically controlled to be from about 16 to
about 25, and preferably from about 16 to about 18 prig.
More importantly, successful flow meters employed
in conventional mass flow controllers typically operate on
a principle wherein heat is transferred Tory withdrawn from
a flowing gas, and a temperature, differential-,.,indùced at
different points in,the,lin,e of flow of the gazebo change
in the flow rate of the gas is employed to impart changes in
the conductivity of a sensor proportional tooth- - -
change in flow rate of the gas. It-has been -found that
fluctuations in the temperature of the assist enters the
flow meter will cause-error in the thermal sensing mechanism
of such flow meters, particularly when operated under the
conditions described herein on the order of.about.l.5~ of the
mass flow rate for each C fluctuation in the adsorb ate
temperature. This error accumulates over extended periods of
time to the extent that it significantly affect's the accuracy
of the flow rate sought to be determined. It has also been
found that fluctuations in the temperature of the environment-
twig. room temperature) over extended periods of time, as
employed for the adsorption and resorption modes described
herein, also cause a relatively large accumulated error in
the mass flow rate relative to the preset value of the flow
rate due to disturbances in the flow meter thermoresponsive
sensing mechanism and the electronic circuitry of the flow
controller. The combination of the aforedescribed errors
precludes achieving substantially constant mass flow rates
as described herein with conventional mass flow controllers
-38-
t;7Sl
under the entire range of conditions at which the methods of the
present mention are conducted.
Accordingly, a mass flow controller which it capable of
achieving substantially constant mass flow rates as described
herein is disclosed and claimed in US. Patent 4,487,213.
A preferred embodiment of this mass flow controller is
illustrated collectively in FIGURES 3 and 4. The integration of
the mass flow controller 301 into the apparatus of the present
invention it illustrated by FIGURE 2.
Referring to FIGURE 3, except for pressure controller 311, the
components of the mass flow controller are housed in a temperature
controlled box 119. This box encloses an inner space 608, which
it in fluid communication with the atmosphere outside the box via
vent 601 and hence is typically filled with air. The box is
typically made of a sturdy material such as sheet metal and
typically encloses a volume of about 2500 cc.
The temperature of the atmosphere within the box preferably is
maintained above ambient room temperature to permit active control
of the box temperature and thereby maintain such temperature
constant. Typically, this temperature is maintained between about
35 and 45C (eye. 39C) to avoid damaging the electronics housed
within the box and to provide a sufficient temper gradient
between the atmosphere within and without the box that when room
air from outside the box is drawn into the same by fan 407, a
dynamic temperature equilibrium can be established within the
box. Thus, the box temperature selected preferably will be above
the temperature which the box would attain, absent a separate heat
source, due to the heat given off by the electronics of the mass
flow controller. Consequently, when air from the external
environment of the box is mixed with air in the box and heated as
described herein, the temperature equilibrium
- 39 -
I
--Jo--
established within the box is not disturbed by the mass
flow controller electronics.
Temperature control within the box is achieved by
the combination of thermistor 404 which preferably is attached
to the base of flow controller block 403, Proportional
Integral and Derivative thereinafter POD) Controller 405,
heating strip 406, and fan 407. Thermistor 404 senses the air
temperature within the box over a temperature range of 0 to
100C and generates an electrical signal proportional there-
to which is sent to the POD controller. The POD controllertRFL model AYE) is preset to generate an electrical signal
proportional to the difference between a preset box them-
portray and the actual box temperature The POD generated
electrical signal activates a heater st~ip~4~6~(e;g;, of the
resistive type 300 watt ~apacityj. Thus, the strength of the
electrical signal from the POD consoler the heater gets
progressively weaver as the actual box temperature apt
preaches the preset temperature and the signal is sub-
staunchly constant'when'the actual box temperature equals
the preset temperature to compensate for toe heat loss to the
environment. This provides extremely accurate temperature
control. The fan 407 runs continuously ~u'ring~operation of
the mass flow controller and circulates air in the box around
the heating strip at a high rate of from about to to 100 (erg.
10-75) times the volume of the box per minute or higher. The
fan 407 preferably is located close to vent 601 to draw fresh
air into the box 119.
Controlling the temperature of box 119 performs at
least four important functions, namely, (1) it heats incoming
gas in line Z01 so that by the time it reaches the flow meter
sensing coil 411, it is at the same constant temperature as
the box 119 irrespective of fluctuations in the room them-
portray; (2) it compensates for the temperature sunsuit-
viny of the electronic circuitry present in circuit board
401, thermal valve 302, and pressure transducer 108 (dyes-
crime hereinafter); (3) it assures that the temperature of
the gas in line 210 is constant at the point where measured
-40-
'So
-41-
by pressure transducer 108 and (4) it eliminates the effect
of changes in ambient temperature on the gas within the
chamber line volumes housed within the box 119 as depicted in
FIGURE 2, which changes would otherwise cause error in the
measurement of the pressure of the gas within these lines. TO
assist box 119 in performing functions 1 and 3, line 201 is
adapted to form coil 213 and line 210 is adapted to form coil
212. Coil volumes, (i.e. of the internal channel of the coil)
of 0.5 cc for coil 213, and 0.8 cc for coil 212 are suitable
to permit temperature equilibration of the gas in the coil to
the box temperature.
The mass flow controller itself, is depicted as
block 301 in FIGURE 2. The input-of mass flow controller 301
is connected to line 201', which contains pressure controller
311 (SURETY TM model 204) engaged in series therewith for
maintaining the,pressure,of thetas entering the mass flow,
controller substantially constant,' and- the output line
202. Mass flow controller 301 is illustrated in more detail
in FIGURES 3 and 4. Referring to FIGURE 3, the primary come
pennants of the mass flow controller include (a) stainless steel block 403 adapted to contain sensing conduit aye which
runs along the length thereof until it connects with thermal
valve 302, sensing coil 411, and the controllable aperture
portion of thermal valve 302 located downstream of sensing
coil 411; (b) circuit board 401 which contains the electronic
circuitry of the flow controller including, detector bridge
circuit 408, linearize 409, amplifier 410, and comparator
controller 600; and (c) thermal valve 302. Pressure
controller 311 is a necessary but auxiliary component
of the mass flow controller.
Gas is introduced and withdrawn from sensing con-
dull aye via conduit lines 201 and 202 respectively. Son
sing conduit aye starts at the entrance to block 403,
passes through sensing coil 411 Which is shown as a single
coil in FIGURE 2, but is more specifically shown in FIGURE 3
as two separate coil sand connects with the inlet portion of
thermal valve 302. The outlet portion of thermal valve 302
-41-
l~tj~7~
it connected Jo line 202 by which gas then exits block 403. The body and electronic circuitry ox t~lecmal valve is seated on top of
block 403 and encased in plastic housing 412.
The preferred thermal valve is available from Dylan
Corporation and is described in detail in US Patent No.
3,650,505.
Circuit board 401 is encased in plastic housing 402.
The circuitry and operation of the mass flow controller is
best described with reference to FIGURE I. Broken line ~16 of
FIGURE 4 depicts the flow meter portion of the flow controller
which contains bridge circuit 517 coupled by sensing conduit
aye. The bridge circuit is of conventional design and it formed
of a first bridge resistor 501 and a second bridge resistor 502.
The bridge circuit further comprises an upstream sensor element
aye and a downstream sensor element 411b. The sensor elements
aye and 411b are wound around the sensing conduit aye adjacent
each other with the upstream sensor element aye closer to input
end 518 of tube aye and the downstream Sonora element 411b closer
to the output end 519 of conduit 202.
The bridge circuit 517 also comprises a DO power supply and
converter 506, (which operates from AC power source 507) which is
connected at one side via line 604 between the junction of the
sensor elements aye and 411b. The other side of the power supply
is connected through a switch 505 to the junction of the bridge
resistors 501 and 502. Output signals from the bridge circuit are
coupled at a first output terminal 503 and a second output
terminal 504. The first output terminal 503 is connected to the
junction of the upstream sensor element aye and the first bridge
resistor 501, and the second output terminal 504 is connected to
the junction of the downstream sensor element 411b and the second
bridge resistor 502. The upstream sensor element aye and the
downstream sensor element 411b are formed of temperature-sensitive
- 42 -
ho
75~ -
-43-
resistance wire which is wound around the outer diameter of
the conduit aye. Such wire can be an iron-nickel alloy,
e.g. Bullock (a trademark of the Wilbur-Driver Company).
The above circuit design is conventional with
the exception that the inner diameter of sensing conduit
aye is of capillary size of typically not greater than
about 0.2, preferably not greater than 0.05 and most pro-
fireball not greater` than about 0.-02 mm and ranges from
about ZOOS to about I , preferably from Abbott
about 0.1, and most-preferably from about 0.01 to about
0.05 mm to achieve substantially constant fluorite. Fur-
therm ore, because of the tow pressures and flow rates handled
by the flow meter, a by-pass tube conventionally employed in
mass flow meters should be avoided. It has been found that
if the inner diameter of sensing conduit aye is too large,
the density of the gas within the tube becomes so low at the
pressures and flow rates described-herein that the thermal
conductivity of the gas drops to the punter the thermal
sensing mechanism (described hereinafter) of the-flo~Y meter
is disrupted and-substantially constant flow Late may not be
attained. - : ''' '
The coupled-bridge circuit output signals 503 and
504 are connected to linearize 409 which electronically
provides a linear output voltage as a function of mass flow.
This voltage is applied through amplifier 410 to comparator con-
troller 600. The linearize, amplifier, and co } atop controller are
all conventional.
In-operation, when the switch 505 is closed, cur-
rent flows through sensor elements aye and 411b causing
the sensor elements to generate heat, thereby raising the
temperature of the tube aye adjacent the elements. Heating
of elements aye and 411b also raises their resistance. At
zero fluid flow through the tube aye, the temperatures of the
sensor elements aye and 411b are equal and the bridge is
therefore balanced, producing a zero output voltage across
the terminals 503 and 504. As fluid enters the input end 518
of the tube aye, heat generated by the elements aye and 411b
is carried by the fluid downstream toward the output end 519
-43-
'75~
of the tube aye. Thus, a temperature diEeeential it created
between the elements Ella and 411b due to the shifting temperature
profile along the tube aye. As the flow of fluid increases in
the tube aye, the temperature of the upstream element aye as
well as its resistance decreases while simultaneously the
temperature of the downstream element 411b, as well as its
resistance, increases. The bridge output voltage at terminals 503
and 504 therefoc increases in needy linear proportion to the flow
rate. After linearization and amplification of the bridge output
voltages of terminals 503 and 504, amplifier 410 applies a jingle
linear voltage which corresponds to the absolute value of the maws
slow rate of the gas before the gas reaches thermal valve 302.
The voltage comma amplifier 410 is applied to comparator controller
600 where it is compared to an external electrical command signal
514 from command signal source and selector 520 which has been
preset to correspond to a selected mast flow rate. The comparator
controller establishes the difference, if any, between the command
signal voltage and the amplifier voltage and utilizes it to power
the actuator aye of thermal valve 302 via line 603. The thermal
valve actuator is thus controlled Jo that it opens more when the
comparator control indicates that the mass flow cave is
insufficient to balance the command signal, and it Clyde more
when the opposite situation occurs.
When the command signal is selected using selector 520, the
latter Allah end a digital signal via line 132 to computer 117 of
FIGURE 2, representative ox the flow rate which has been selected
and which has previously been calibrated with a blank run.
In a more preferred alternative embodiment sensor elements
aye and 411b can be combined into a jingle coil containing a
center tap as illustrated in Us Patent No. 3,938,384. By
utilizing a single coil with a center tap rather than two separate
sensor elements, it is possible to space the coils close
together. Thus, heat loss is reduced, equalization between the
upstream and downstream sensor
- 44 -
us.,'
I -
elements is facilitated, and the gain of the circuit (them-
portray change per unit of flow) is greater. In add-
lion, the response of the circuit is faster, and the range
of useful flow measurement and the linearity of the air-
cult is increased..
An optional feature of the circuit illustrated
in FIGURE 4 is volt meter 510 connected across the coupled
output terminals-503 and 504. The electrical signal from
.
the volt meter is converted freemen analog signal to a
digital BUD signal by a converter (not shown and the BUD
signal is sent to computer 117 of FIGURE vow line 303.
During the blank calibration run, the computer samples the
output from volt meter 510 over period of about 10 mint
vies, during which period it acquires data a a rate of
about 1 data point per second and averages the acquired
data which is stored in a data base as calibrated value
.. .. ... . ..
During an adsorption or resorption run, the computer compares
the calibrated value with-the actual value sampled from the
volt meter during the ad-or resorption run in order to
,. . .
determine if the run is cordite reliably. This issue
quality control feature which permits observation of any
deviations from the desired flow rate after completion of the
run.
It is to be understood, that while the mass flow
controller has been described with respect to a particular
flow meter, other types of flow meters can be used which
provide an electrical signal us flow function, such as
described in US. Patent Nos. 3,650,151; 4,056,975; 4,100,801
and the like. While a thermal valve as described herein is
30. preferred to regulate the flow rate, any other electrically
actuated means which possesses the sensitivity and copyboy-
lily of regulating the flow rate to be substantially con-
slant at the conditions of use described herein can be
employed. Similar considerations also apply with respect
to the mass flow controller itself. The present invention
requires the capability of achieving a substantially cons-
lent flow rate throughout the range of conditions of low
-45-
it it
-46- -
flow rates and low pressures, over extended periods of
time described herein. While it is believed that the
inventors herein are the first to develop devices with
such capabilities, the method and apparatus of the present
invention does not preclude the use of alternative means
which perform the necessary functions of the mass flow
controller and associated environmental control box should
they be developed. - - -
Returning to FIGURE 2,-gas passing through line 201
located within environmental control box 119, passes through
coil 213 wherein its temperature equilibrates with the them-
portray of said box 119, passes through flow controller
301, wherein its rate is regulated as described herein indenters the sample holder 109-of the sample holder section via
lines 208, 209, vacuum solenoid valves 4,-and 5, and stopcock
19 .
The sample holder section comprises sample holder
109, liquid bath container 111, liquid level controller 113
20, and liquid bath 112. Sample holder lo typically is a
glass flask of about 20 ml in volume having a glass capillary
neck 122 about 2 mm inner- diameter. The capillary neck
terminates with a ground-glass joint 123 adapted to receive
male ground glass joint 124 of line 125. To add or remove
sample 110 to or from sample holder 109, ground glass joints
123 and 124 are disconnected. The assembly (referred to
herein as Assembly A) comprising ground glass joint 124, line
125, which is connected to stopcock 19, which is connected to
line 126 and its associated ground glass joint 127, is used
for sealing and/or connecting sample holder 109 to either the
outguessing section, eat ground glass joint 21, or to the
mass flow controller section at the end of line 209 using
ground glass joint 128, e.g.,Assembly A permits sealing a
sample holder that contains a sample by closing stopcock 19
after outguessing and evacuation. Thus, Assembly A and sample
holder 109 permit sealing and transfer of sample holder 109
to the desired location in the apparatus.
-46-
-47-
Liquid bath container 111 typically is a dower
flask capable ox holding the liquid bath, such as liquid
nitrogen, and large enough to accept immersion of sample
holder 119 therein when it is connected to the mass flow
controller section. As described above, the liquid bath
112 is typically liquid adsorb ate or desorbate, and when
the level 129 of the bath 112 is maintained constant in
liquid bath container ill during ad-or resorption, the
bath 112, serves to control the temperature of sample
holder 109 when immersed therein. The level 129 of bath
112 in relation to the depth of immersion of sample holder
109 also dictates the volume-of the sample holder So in
equations 1, 2 and 3 while the heath 112 temperature sets
the temperature To Andre Tess. in the same equations.
For example, container ill is filled with sufficient bath
112 so that the-bath level 129 in container 112 intersects
the capillary neck 122 of sample holder 109 at point 130
on said capillary neck 122. The location of point 130
typically is midway between ground glass joint 123 and the
termination ox the capillary neck of sample holder 109 at
point 132. Sample holder rack 131 is set within container
111 to stabilize the sample holder and assure that the
sample holder lay is immersed to the same depth within
bath 112 fox each run when the bath level 129 is constant.
Thus, ASH is the volume of sample holder 109 which is
immersed in bath 112, i.e. the volume of capillary neck
from point 130 to 132 + the volume of the remaining non-
-capillary volume of sample holder 109.
The level 129 of bath 112 in container 111 is held
constant with a conventional liquid level controller such as
a Huntington Electronics In Model 200, collectively depict
ted as bath level sensor 113 and control valve 20 actuated
by sensor 113 adapted for use herein. For Example, when
employing liquid nitrogen as the liquid bath, the liquid
nitrogen tends to evaporate during the course of the ox-
pediment. Consequently, additional liquid nitrogen must
-47-
I .
be added to maintain the bath level substantially constant.
Accordingly, bath level sensor 113 senses a change in the bath
level and activates control velvet allow fresh liquid to
enter lines 308 and 310. However, as liquid nitrogen enters
lines 308 and 310, the tempexature'of the lines is warmer than':
the liquid nitrogen thereby causing the nitrogen to evaporate
explosively. Liquid and vaporized nitrogen would therefore
ordinarily be violently discharged into the liquid bath 112
. thereby upset tithe bath lovely This causes error in the.
pressure recorded as a function of time It has been found
that this problem can be eliminated quite effectively by
installing a vent Lyon which- effects separation of the
fresh bath vapor from the fresh bath liquid..before~the fresh
bath liquid enters the liquid bath.container.'This procedure
maintains the bath level substantially constant-within a
deviation of about. _ 0.5 mm. : Thus -as liquid bath 112
evaporates, control valve 20 receives fresh liquid from line
307 which is connected to a source of the liquid bath (not
shown). Bath liquid passes from control valve 20, through
line 308 and into line 310, the open end of which is-immersed
in the liquid bethel. Line 309 is a vent open to the
atmosphere and in fluid communication with lines 308 and 310.
The end of line 310 has a glass wool plug inserted therein to
create a back pressure and cause any vaporized liquid bath to
exit via vent line 309 rather than be discharged violently into
liquid bath 112. This avoids upsetting bath level 129 and is
a way to maintain the bath level substantially constant. By
maintaining bath level substantial constant, the volume
US H at temperature To H. is also held substantially con-
slant.
Accordingly, by the combined use of box 119 to
control the temperature of the chamber line volume, and
the liquid bath to control the temperature of the sample
holder volume, the total chamber volume, and the gas con-
twined therein is maintained at a substantially constant
temperature. sty substantially constant temperature as apt
plied to the total chamber volume is meant deviations, if
-48-
_99_
any, in the average temperature of the total chamber volume
of typically not greater than + 0.35, preferably not greater
than + 0.20 and most preferably not greater than 0.17% of said
average temperature value.
The primary components of the pressure sensing and
recording suction of the apparatus comprise pressure trays--
dicer 108 (SETR~TM 204 AYE) and a-pressure recording
device such as computer 117 (Apple ITEM)' Andre strip
recorder 118. Pressure transducer 108 is located in envier--
on mental control box lit and the input end hereof is-con-
netted to line 208 (located between vacuum`selenoid valves
4 and 5) by line 210 and coil 212, 'aid coil Allis being
located within environmental control box 119-.-- Lyon Isis
fluid communication with the sample holder during both ad-
sorption and desorpti~n. within coil 212 the gas in line
210 is heated to the equilibrium temperature of box 119.
Thus, some of the gas f-lowing in Lyon passes through line
210 and coil 212 and contacts the input end of pressure
transducer 108. The temperature of the gas in coil 212, i.e.
the box temperature, is therefore-constant, and changes in
pressure in line 210 reliably reflect changes in pressure in
the sample holder 109. The pressure transducer 108 senses the
pressure in line 210 at constant temperature, and converts
the presort an electrical signal which is passed from
the output end of pressure transducer 108 to the input end
of interactive structures A/D model A convertor 121
via line 304. Converter 121 changes the analog electrical
signal from pressure transducer 108 to a digital electrical
signal. This digital signal is passed from the output end of
converter 121 to digital computer 117 via line 306.
Optionally, the output analog electrical signal
from pressure transducer 108 can be passed to strip recorded
118 via line 305.
Computer 117 and strip recorded 118 are alter-
native means for recording the pressure of the gas being
introduced or withdrawn from sample holder 109 as a lung-
lion of time and can be used alone or in combination.
-49-
Jo
-50-
However, the use of a computer is preferred.
Accordingly, for the adsorption mode the computer
117 is programmed to enable it to. (a) record, typically
on a semi continuous basis, digital pressure signals received
indirectly from pressure. transduce 108 as a function of
time to establish and store a first data base of pressure
vs. time; (by establish and store a second data base of
several different mass flow rates, one.of.:which.is--selacted
by the computer operator convert the pressure vs.
time information in the first data base and the selected
mass flow rate in the second data base to-a third data
base of all or~part.of the. adsorption isotherm, i.e. Vats
v. (Pups) an store thyroid data base: and (d) calculate
the surface.area:of`a sample using, for example the BET
equation from the information in the 3rd..data base. '.
For the desorption.mode,.computer:.117 -is programmed
to establish and store the first and second data bases
described above in connection with the adsorption mode,
during operation of the resorption mode..: The computer
then establishes and Strauss 3rd.data'base of the desorp~
lion isotherm, i.e., VdSb v. (Pups). and uses the 3rd data
base to calculate the pore size. distribution of the sample
using, for example, the Kelvin equation, and the total
pore volume using Equation 11.
To establish the first data base described above
of pressure vs. time,. the computer samples and stores
digital pressure signals during an ad~or.desorption run on-
a semi continuous basis:. The frequency of sampling is
controlled by the operator. The particular frequency
selected is described herein.
To establish the second data base of mass flow
rates described above, the command voltage source and
selector 520 is calibrated at about 12 different voltage
settings using blank runs and the actual mass flow rate
-50-
I
-51-
for each blank run is determined. The 12 flow rates em-
plowed typically will vary from about 0.2 to about 0.7
ml/min at STOP The computer is then programmed with
these calibrated flow rates, and a digital voltage associated
with each command voltage. I
Consequently, when the operator selects one of the-
calibrated command voltage settings for a run the command
voltage selector 520 automatically sends the corresponding
digital signal to the computer 117 via line 132 represent-
live of the selected flow rate. The computer uses
this information to determine what mass flow rate should
be employed to calculate the amount of gas ad-or resorbed
as described herein. The ability of a computer to auto-
magically perform the affronted operations is another
advantage of, and made possible by, the use ox a sub Stan-
tidally constant mass flow rate. --
The computer also performs several additional functions which serve to automate the system completely.
Thus, the computer manipulates many of the lung-
tonal components of the apparatus, including: opening and closing-selenoid valves for: selection of gas from
the gas supply section; introduction or withdrawal of gas
from the sample holder 109; evacuation of sample holder
during outguessing; and saturation of the sample with con-
dented gas preparatory to a resorption run. The computer
also controls outguessing conditions, such as temperature
and duration.
The vacuum section supplies the vacuum to outguess
the sample, evacuate the sample holder, and resorb the
desorbate from the desorbent. The vacuum section comprises
a mechanical and a diffusion vacuum pump collectively shown
and referred to as vacuum pump 105, and pressure
gauge 120 (Edward CP25 Gouged). The mechanical pump
ovarian 0401-K6820-301) reduces the pressure in line 204 to
10-3 mm Hug, while the diffusion pump ovarian 0160-82906-301)
disposed in series with the mechanical pump, reduces the
pressure to the desired level of 10-7 to 10-8 mm Hug.
-51-
52
The pressure gauge 120 reads the pressure directly
from line 204 as a check on the proper functioning of the
vacuum pumps. The vacuum end of vacuum pump 105 is con-
netted to the apparatus via line 204 which connects with
lines 205 and 203. By appropriately opening and closing
vacuum solenoid valves 1 and 2, the outguessing and adsorb-
tion/desorption sections can alternately be engaged with
vacuum pump 105.
The outguessing section comprises aluminum heating
block 14, one or more conventional cartridge heaters 115,
vacuum solenoid needle valve 11, and ARC. power source 16
to supply current to the cartridge heaters. The aluminum
block is milled to provide a space 114 adapted to accommodate
sample holder 109'. While only one spate 114 and one
sample holder 109' is shown, aluminum block 14 typically
is adapted to receive and heat 4 sample holders. Assembly
A, comprising ground glass joint 127', capillary line
, 126', stopcock 19', capillary line 125' and ground glass
- joint 124' permit interfacing the sample holder 109' with
the vacuum section via ground glass joint 21, electrically
operated vacuum solenoid 11 and line 2Q6. To add a sample
to sample holder 109', Assembly A is disconnected, the
sample 110', added to the sample holder 109', and Assembly
A reconnected, as shown.
To outguess the sample the vacuum pump 105 is
started, stopcock 19' is opened, solenoid valve 1 is closed,
vacuum solenoid valve 2 is opened, and vacuum solenoid
valve 11 is initially opened intermittently to avoid suck-
in sample 110' out of the sample holder. The cartridge
heaters are engaged and the sample heated under vacuum
until outguessing is completed. Stopcock 19' is then
closed while the sample holder is still under vacuum to
maintain the sample 110' in the evacuated state while
being transferred to the adsorption/desorption section.
Solenoid needle valve 11 is then closed, and Assembly A
Chile connected to sample holder 109', is disconnected from
ground glass joint 21. The sample holder-Assembly A combine-
lion is allowed to cool and then connected to the adsorption/
-52-
I
-53-
resorption section as discussed.
All gas conduit lines illustrated in FIGURE 2 are
constructed of 0~05 to 0.2 inch I.D. stainless steel tubing
up to metal lass connectors 135 and 136. All lass gas
conduit lines are capillary lines of about 2-6 mm inner
diameter and 7-12 mm outer diameter. All solenoid valves are
conventional electrically actuated vacuum valves (Hardman-VA-
Allah with the exception of valve 1 which is an air
operated valve (ASCOTM').'and valve 11 which is an electrically
operated needle valve (WhiteyTM); -valves 4 and 2 are put
in backwards because they work in only one direction. If
pressure is applied to the low pressure side of these valves,
they act as a check-valve. All metal joints are welded where
possible.
For the adsorption mode, line volumes constituting
AL in equations 1,-2 and 3 which must be known a~e.those
defined between valve-302 and point 13'0 on line 122, including
lines 202, ~08, 209, lZ6, 125, Andes well as lines 210 '
and coil 212. .
I! 20 or the resorption mode, valve 4 will be closed and
the circuit of line volumes starting from valve keenest-
tuning AL in equations-l, 2 and 3 which must be known are
coil 213, lines 201, 207, 208, 209, 126, 125, and 122 up
to point 130 online 122, as well as line 210 and coil 212.
Representative volumes include: from valve 19 up
to and including sample holder 109 about 20 ml; from valve 19 to
mass flow controller 301 about 19 ml; from exit of box 119
in line 209 to point 130 on line 122 about 0.6 to 0.8 ml; lines
201 and 207 including coil 213 about 4 ml; and in line 210 and
coil 212 about 7.5 ml. Thus from FIGURE 2 it can be seen that
by locating lines 201, 202, 208, 210 and 207 within box 119,
only a very small fraction of the line volume critical to
pressure measurements is exposed to room temperatures and
associated fluctuations therein. The effect of such fluctuations
is therefore minimized to the extent that they can be ignored.
-53-
I
-5q-
Accordingly, it is preferred to maintain from about 94 to
about 99, and preferably from about 96 to about 98~ of the
chamber line volume, within box 119, excluding any chamber
line volume below bath level 129.
At the start of the adsorption run, outguessing
has been completed, valve 2 is closed, and evacuated sample
holder 109 and Assembly A are connected to ground glass
joint 128 with stopcock 19 closed. The sample holder 109
is therefore appropriately situated in the liquid bath.
Valves 1, 4, 5 and 6 are then opened and vacuum pump 105
started to evacuate the system. After about 5 minutes,
evacuation is completed, and stopcock 19 is opened while
valves 5 and 6 are closed. Valve 3 and one of valves 7 to
10 are then opened to stabilize the mass flow controller
which takes about 5 minutes. The appropriate command
voltage is selected, valve 1 is then closed and valve 5
opened at the same time. Adsorb ate flows into the sample
holder from line 211 tracing an input path defined by the
open and shut valves described at this point, and the
pressure will start to rise. Appropriate measurements of
pressure vs. time are made and the surface area of the
sample is taken.
To conduct the resorption mode, the outguessed
sample containing sample holder 109 is in place as described
at the start of the adsorption mode. Valve 2 remains
closed during the entire operation. The system is evacuated
by opening valves 1, 4, 5, and 6. Stopcock 19 is then
opened. The sample is then saturated with desorbate by
closing valves 1 and 6 and opening valve 3 and one of
valves 7 to 10 to select the appropriate adsorb ate. Valves
4 and 5 remain open during saturation. The mass flow rate
can be initially high since pressure readings are not
taken during saturation when only the resorption mode is
to be conducted. Saturation generally will take a long
time, e.g. about 1 to about 8 his. because all of
the pores of the sample must be filled with liquid decor-
bate. However, as a matter of convenience, care should be
taken not to over saturate the sample to the extent that
-54-
-55-
desorbate condenses on the sample holder 109 wall. Such
an occurrence will unnecessarily prolong the resorption
mode duration. When the sample is saturated, the desorp-
lion mode can start. Resorption is initiated by closing
valves 3 and 4 and opening valves 1 and 6, valve 5 remaining
open. The configuration of opened and close valves is
necessitated by the fact that the mass flow controller
operates in only one direction. Consequently the vacuum
section must pull the desorbate through the mass controller
in its forward operating direction. If the sample is
properly saturated, the desorbate pressure will remain
constant for several minutes. For calibration calculations,
t = 0 at the moment the pressure starts dropping. It is
at this moment that any and all of the condensed desorbate
on the sample holder wall and in between the sample particles
is removed. Pressure sensing and recording, however, is
initiated at the same time as resorption.
To conduct combined adsorption and resorption
modes, the adsorption mode is employed to saturate the
sample and pressure vs. time readings are taken during
both adsorption and resorption.
The following examples are given as specific
illustrations of the claimed invention. It should be
understood, however, that the invention is not limited to
the specific details set forth in the examples. All parts
and percentages in the examples as well as in the remainder
of the specification are by weight unless otherwise
specified.
In all of the following examples the apparatus
in its preferred embodiment as described in connection
with the description of FIGURES 2, 3, and 4 was employed.
Example 1
This example illustrates a blank calibration run
for the adsorption mode repeated 3 successive times and
the invididual plots overlaid on each other in FIGURE 5.
The following Table 1 lists the appropriate parameters
employed .
to i'
-56-
Table 1
Adsorb ate No
Saturation Pressure 760 mm Hug
Chamber Line Volt AL) 20.01 cc.
sample holder volt ASH 21.60 cc.
Lit. No bath Temp. (To H,) 77.2 OR
Line Temp. (TO) 296.0K
Partial Pressure Range 0 to 0.263
No. of Pressure/time data 1,260
points sampled
lo The run is conducted as described for the adsorb-
lion mode. The flow rate was calculated from equation 1 to
be 0.5 ml/min at 5TP. Plots of the pressure vs. time
generated by a Hewlett Packard AYE plotter hooked up to the
compute rare provided at FIGURE 5. As may be seen therefrom
a straight line results representative of a substantially
constant mass flow rate. The degree of scattering of data
points is calculated by (1) determining the absolute value
of the deviation of the pressure value for each data point
from the pressure value that corresponds with the best
straight line through all the data points; (2) averaging
the absolute valves of the deviation; (3) relating this
average to the pressure in the system and expressing this
value as a percentage. - -
The degree of scattering is away of expressing
the constancy of the flow rate. For this example, the
degree of scattering for all three plots was 0.8%.
Example 2
This example illustrates a blank calibration run
for the resorption mode. The following Table 2 is lists of
the appropriate parameters employed:
-56-
- 57 - -
Table 2
Desorbate No
Saturation Pressure 760 mm Hug
Chamber Line Vol. TV 36.68 cc.
Sample holder vol. (Us ) 21.60 cc.
Lit. No bath Temp. TUSH 77.2 OK
Partial Pressure range (Pups) loo to 0
Line temp. (TO) : 296 OK
No. of pressure/time data punts 30,000
sampled
The mass flow rate was calculated to be 0.30 ml/min
with a degree of scattering ox P.24% . A plot of
pressure vs. time generated by the computer and plotter is
provided as FIGURE 6. As maybe seen therefrom the plot
is divided into 3 segments A, B, and C. Segment A repro-
sets the constant pressure caused by evaporation of con
dented desorbate within the sample holder. At the end of
segment A all condensed desorbate has been removed and the
plot abruptly shifts slope which remains substantially
constant throughout segment 3. Thus, segment B represents
withdrawal of desorbate at a substantially constant rate.
At the end of segment B and at pressures near
absolute vacuum the slope again shifts. It is at this
point when the mass flow controller is unable to maintain
the flow substantially constant. However, this does not
occur until a partial pressure (Pups) of about 0.02 is
reached This partial pressure is well below that needed
to obtain enough of the resorption isotherm to calculate
the pore size distribution of the sample and provide a
substantially complete resorption isotherm.
Example 3
This Example illustrates an actual adsorption run.
The sample chosen for the surface area determination is a
silica-alumina ASTM Standard No. N10074 having a reported
surface area of between 281 to 297 mug depending on the
method used for the determination. previously calibrated
blank was employed to determine the mass flow rate. The
-57-
-58-
sample was outguessed in the sample holder under vacuum at
400C. for 700 min. The appropriate parameter of the
adsorption run of this Example are summarized below in Table
3.
. Table 3
Adsorb ate No
Sample type silica-alumina
Sample weight. . 1.074 I)
. sample density 3.2 gag
Saturation pressure 760.00 (mm go
Chamber line vol. AL 20.01 cc
Sample holder vol. (Vs.H,1 21.60 cc
Lit. No bath Tempt TO 77.~ OK
Line temp. (To 315 OR
Mass flow rate 0.30 (ml~min~
Partial pressure range 0 to 0 ~63
Total no. of pressure time
data points sampled 25~440
Of the total pressure/time data points sampled
by the computer, 10 approximately equidistant sampled chamber
pressure points on the plot are reported herein for convenience
at Table 4. The actual plot is shown at FIGURE 7. The reference
pressures corresponding to the reported sampled chamber pressure
are also directly shown at Table 4. The volume of adsorb ate at
SUP adsorbed per gram of sample, as well as the relative adsorb ate
pressure (Pups) at which this amount is adsorbed, is calculated
from the difference between the CUP and SOP using equation 2 and
the entire pressure time data base.
:: -so-
_ 59
. . .
. O O O I O O N o o o
Pi o o o o o I o o o o
_, _ o I o o I o o o o o
. .
I ED CO I a ED
_. - .. o . or ED a ED . or , . .
X I, o I>, o o , I I I I
. I Us' Jo o o o Cal I I o
o
. Q.
ox it or ox ox
Al In co I us us ED to
0 lo a ox Ill lo us r 0 R
Us I) Us Us I ED I I O try W .'
Lo ED ED r` I_ a Jo
ox
V pi .
V o o I o to us o o o o go R
I O I I n It I I I_ I
a
,
F.. I h ::~
_ I R us us
I OX to I O I`
I_ or Us Us ED r- I_ a a
. ray a
Il`~lllil
~,~.
O O Us ED r- Clue Ox O CAL;
I
--59--
- 60 -
.
- The linearized version of the BET equation is plotted
from Relative Pressure ~x-axls) and as the y-axis the
value calculated for.
Pry
Pry
at each relative pressure.' The slope, and y-inte~cept of
the ploy were calculated to be 0~.000 and O.Ol5respectivelyO
The surface aria was then determined to byway McKee.
Example 4
This example illustrates the des,orp~ion mode and
employs 3 different runs In the first run a sample of
pore glass Sample Assay subjected to the resorption mod.
In Run 2, a different sample of pore glass was used, ye.
Sample B. In run 3, a 50 White % ratio mixture of pore
glass samples A and B-respect;vely was employed, Each
sample was outside under vacuum at 375 C. for 700
min. Each sample was then saturated Wyeth No disrobe
until a sample saturation pressure as reported in Table 5
was attained in the sample holder., Resorption was then
commenced at the mass flow rate reported in Table S. The
computer samples the Dickerson pressure as a function of
time at a frequency of about 60 data points per minute
and plots pressure YE. time as provided in FIGURE 8. In
FIGURE 8, plot 1 corresponds to Sample A, plot 2 to Sample
B, and plot 3 to the mixture of samples A and B. Plot 3
illustrates toe high degree of resolution, obtainable from
the method and apparatus of the present invention, between
the pressure/time profile attributable to sample A and
that attributable to sample B. More specifically, segment
A of plot 3 corresponds to segment a ox plot 1 and segment
B of plot 3 corresponds to segment b of pot 2. The extent
of this resolution is more clearly seen, however, from the
pore size distribution plot of ~V~sb/~Rp as provided it
FIGURE 9 from the data of plot 3. As may be seen from
FIGURE 9 the pore radius of sample A in plot 3 of FIGURE 8
is predominantly 81 angstroms and the pore radius of
-60-
to
- 61
.
sample 8 in plot 3 of FIGURE 8 is predominantly 55 angstroms.
This corresponds with the pore size distributions obtained
from plots 1 and 2. A summery of the appropriate test con-
doughtiness is provided at Table 5.
It will be noted that a discontinllity appears in
the plots of FIGURES S and 7 at a pressure of about 140 mlllHg,
These discontinuities are a consequence of the attuning
effect of the A/D converter used in generating
FIGURES 4 to 8 and are not caused by the raw data which are
10 used as a basis of the calculation.
--61--
-- 62 --
m o O o O
03 Us ED O
. . I_ . . I., . . .
O Z O I`
- : O O
CO O o I 0:,
- o I o
a: . . Jo z . . "
O 1--; 0 ED I to
o o
. O O I
I 0 ED O
D Z . . , ,, , ,
o t-- o I
. . _ . - (I N 1` --1
Us . _'
a) .
.,
Eye
E to o
E ^ _ I- Pi.
O I
, Us
O D.... 3 -- a Lo
_ O
5' --' O I E O
-- - I o
on v .,
Jo
s I a a) s us
us E C C
.,~ V ,. I I
a ; o m o
Q. 3 MU) S
Jo pa I 1 0
En Lo Q Q I) Z C
a I O O E En
E E En S E
I 0 pa a I: s I -I O
E us 1 a v
U)
- 63
The principles preferred embodiments, and modes
of operation of the present invention have been described
in the foregoing specification. The invention which is
intended to be protected herein, however, is not to be
construed as limited to the particular-forms disclosed
since these are-to be,regarded-as illustrative-rather than
restrictive. Variations and changes may be made by those
skilled in the art without departing from the spirit of
the invention. - -'
.
.
- .. .
.
,
-63-
