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THE THEORY AND PRACTICE OF MEMBRANE EXTRACTIONS

By

Mark Anthony LaPack

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1994

ABSTRACT
THE THEORY AND PRACTICE OF MEMBRANE EXTRACTIONS

By
Mark Anthony LaPack

The selection of a membrane for a given separation of a mixture

is generally based upon the "like-dissolves-like" rule, which often

times is an inadequate guide. In this work, membrane extractions
have been studied using silicone membranes and mass spectrometry.
Aqueous and gas samples were exposed to one side of the membrane
while the contents on the other side were analyzed by mass
spectrometry. Predictive permeation models have been developed.
Good correlations are observed between the permeation data,
chromatographic data, a solubility parameter model, and a model
based on the boiling points of the analytes. The effects of
experimental parameters on membrane extractions have also been
examined. The effects of the configuration of the membrane
extractor, membrane dimensions, temperature, sample flow rate, and
other parameters are presented in the context of optimizing the
. separation technique. A membrane extraction mass spectrometric
technique has been developed for on-line analysis of organic
components of multiple liquid and gas streams, and applied in an
aerobic biological wastewater treatment process. Mass balance
determinations were performed by quantitatively measuring organic

contaminants in influent and effluent water and air streams.

Copyright by
MARK ANTHONY IAPACK
1995

to my Pat

ACKNOWLEDGMENTS

First, I thank my research advisors. I thank Chris Enke for

. sharing with me his wisdom, creativity, encouragement, and his
patience. I also thank Jim Tou for his support and encouragement and
for his keen attention to detail. I will always remember the pioneering
spirit of these two men.

I thank Vicki McGuffin for her enthusiasm, inspiration, and
technical guidance.

For their valuable combinations of critique and encouragement,

I thank Dr. Jack Watson, Dr. James Harrison, Dr. Bill Reusch, and Bob
Bredeweg.

For their complete support of this work, I thank the
management of the Dow Chemical Company, especially Mel Koch, Jim
. Havel, Foppe Dupuis, Marylu Gibbs, Wes Westover, Don Calvin, Paul
Dean, Jackie Kelyman, and Irv Snyder.

To my friends at MSU and in Midland, for their friendship and
encouragement, especially Jane Tou, Jim Shao, Mike DesJardin, Bruce
Bell, Mark Cole, Paul O'Connor, Mark Dittenhafer, Steve Humphrey,
the Enke Group and the Special Analysis Group.

For helping me to keep my priorities in check, I thank my
beautiful children, Makenzie and Daniel.

ii

I am very grateful for the love of my two families in Indianapolis -
especially my mother, father, and siblings, who never missed a chance
to remind me how long I have been in school.

For my wife, Patty, for standing by me, for taking on more than
her share of keeping our home together, and for playing the role of
the single parent.

Finally, I thank God with all my heart for bringing all of these
wonderful people and opportunities into my life.

iii

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER

1 INTRODUCTION
Background
Purpose of this work

2 PERMEATION FUNDAMENTALS
. Steady state permeation
Non-steady state permeation

Organic enrichment

3 THE CORRELATION OF PERMEABILITY TO
HILDEBRAND SOLUBILITY PARAMETERS

The solubility parameter
Development of the theory
Correlation of data to theory

4 A MODEL FOR CHARACTERIZING AND
PREDICTING MEMBRANE EXTRACT IONS BASED
ON CHROMATOGRAPHIC RETENTION

Retention and distribution equilibria
Band spreading and diffusivity
Efficiency and enrichment

iv

12

35

79

5 PRACTICAL ASPECTS OF MEMBRANE 1 1 9
EXT RACTIONS

Membrane dimension considerations
Temperature considerations

Sample flow rate considerations
Extractor configuration considerations

Effects of distance between the extractor
and the analyzer

6 THE APPLICATION OF MEMBRANE EXTRACTION 154
MASS SPECTROMETRY TO THE ANALYSIS OF GAS
AND LIQUID PROCESS STREAMS

Experimental
Multiple gas and liquid stream analysis

Application to a biological wastewater
treatment process

Conclusions

' APPENDIX 1 86

Permeation measurements

LIST OF TABLES

Table 1.1. Membrane separation terms and some analogous terms
used in analytical chemistry.

Table 2.1. Effect of hollow fiber membrane radial dimensions on
analytical response. The silicone hollow fibers were 2.5-cm long.
Temperature = 23 °C.

Table 2.2. Survey of temperature effects on detection limits (S/ N = 2)
- for organic compounds in air and water. The membrane is a 2.5-cm
long, 0.0305-cm i.d., 0.0635-cm o.d. silicone hollow fiber.

Table 2.3. Effects of membrane thickness on response time for gas
phase organic compounds. The membranes are 2.5-cm long silicone
hollow fibers. Temperature = 23 °C.

Table 2.4. Survey of temperature effects on response time, t5o, for

organic compounds in nitrogen. The membrane is a 2.5-cm long,
0.0305-cm i.d., 0.0635-cm o.d. silicone hollow fiber.

Table 2.5. Survey of temperature effects on the enrichment over the
sample matrix for organic compounds in nitrogen and water.

Table 3.1. Molar volumes (vi) and Hildebrand solubility parameters
(81) from References l, 12, and 28.

Table 3.2. Experimental permeation parameters for substances in a
silicone elastomer membrane at 25 °C.

- Table 3.3. Experimental and theoretical distribution ratios for
substances in a silicone elastomer membrane, at 25 °C.

Table 3.4. Experimental and theoretical distribution selectivities for
substances relative to methane and to methanol in a silicone elastomer
membrane at 25 °C.

Table 3.5. Partial molar volumes, v'i, for surface-active functional
groups from Reference 31.

Table 3.6. Data for determining the active volume ratio, V'f/Vp, in a
silicone elastomer membrane at 25 °C.

_ Table 3.7. Experimental and theoretical diffusivities for substances in
a silicone elastomer membrane at 25 °C.

Table 3.8. Experimental and theoretical (D-k model, Equation 3.42)
diffusivity selectivities for substances relative to methane and to
methanol in a silicone elastomer membrane at 25 °C.

Table 3.9. Enrichment factors for compounds relative to methane and
to methanol in a silicone elastomer membrane at 25 °C. Theoretical
values were obtained from the product of distribution (Equation 3.16)
and difl'usion selectivities (D-k model, Equations 3.36 and 3.42).

Table 4.1. Molar volumes, Hildebrand solubility parameters (7, 8, 10),
and boiling points (1 1) for the compounds used in this study.

Table 4.2. Experimental distribution ratios, K1, determined by ME and
GC at 25 °C.

Table 4.3. Values for the heats of solution for selected compounds in
the membrane and chromatographic stationary phases.

' Table 4.4. Distribution selectivities for compounds over nitrogen and
heptane at 25 °C. Tb = predicted from the boiling points (Equation

4.7); SP = predicted from solubility parameter theory (Equation 4.3);
ME = experimental from ME data; G0 = experimental from GC data.

Table 4.5. Mobile phase diffusivities, Dun, and chromatographic band

spreading components used to calculate diffusivities in the stationary
phase at 25 °C.

Table 4.6. Difi‘usivities at 25 °C in the stationary phase for compounds
of interest determined by membrane extraction experiments (ME),
and gas chromatographic experiments (GC).

Table 4.7. Values for the activation energies for diffusion for selected
compounds in the membrane stationary phase.

Table 4.8. Diffusion selectivities for compounds over nitrogen and
over heptane at 25 °C. Tb = predicted from boiling point model
(Equation 4.24); SP = predicted from solubility parameter theory
(Equation 4.31); ME = experimental from ME data; GC = experimental
- from GC data.

Table 4.9. Values for the activation energies for permeation for
selected compounds in the membrane stationary phase.

Vii

Table 4.10. Enrichment factors for compounds over nitrogen and
heptane at 25 °C. Tb = predicted from the boiling point model

(Equation 4.40); SP = predicted from solubility parameter theory
(Equations 4.3 and 4.32); ME = experimental from ME data (Pi/P1);

G0 = experimental from CC data (Equation 4.35).

Table 5.1. Gas permeabilities and permeation rates/ unit concentration
(given per unit ppm by volume) through a 2.54-cm-long, 0.0305-cm-
i.d., 0.0635-cm-o.d. silicone hollow fiber membrane.

' Table 5.2. Permeabilities and flow rates for gases through a 2.5-cm-
long, 0.0305-cm-i.d., 0.0635-cm-o.d. silicone hollow fiber membrane.

Table 5.3. The effects of interface tube length on response.

Table 5.4. Comparisons between response time (t50-t0) and rise time
“2904110) for l-butanol.

Table 5.5. The effects of analyzer conductance on response time.

Table 6. 1. Spike sets with volume % in acetone, monitored ions, and
standard response factors. Baseline response was 0.0005.

Table 6.2. Spike concentrations (mg/ L) in the influent wastewater.

Table 6.3. Concentrations (mg/L) detected in the effluent water and
the air streams in the reactive process. Styrene and chlorobenzene
are not detected (N.D.) above the baseline in the effluent water.

Table 6.4. Percent recoveries and standard deviations for the spiked
- organic compounds.

Table 6.5. Percent recoveries and standard deviations in the effluent
water streams.

Table 6.6. Percent recoveries and standard deviations in the effluent
air streams.

Table 6.7. Percent bio-uptake and standard deviations. Experimental
values corrected for the recoveries in the analytical test reactor
(reactor 2) are given in parentheses.

Table A.1. Mass spectrometric response factors, relative to toluene,
used to determine permeation parameters.

Table A2. Relative standard deviation for each known source of error
and for each computed permeation parameter.

viii

LIST OF FIGURES

Figure 1.1. The components of a typical membrane extractor.
Figure 1.2. A typical membrane permeation response curve.

Figure 2.1. A cross-section view of the general components of the
permeation process.

- Figure 2.2. The mass spectrometric response and pressure vs.
concentration of toluene in the feed stream. Aqueous standard
concentrations are reported on a grams/liter basis while gas standards
are reported on a volume/volume basis. The portion of the toluene in

air response curve labeled ¥ deviates from linearity due to excessive
pressure in the ion source.

Figure 2.3. The effects of temperature on permeability.

Figure 2.4. A plot of solutions to non-steady state permeation
(Equation 2.12), calculated from t50 values, and permeation response

data for chloroform at 26 °C and 85 °C.

Figure 2.5. Normalized permeation response curves for 1,2,4-
trichlorobenzene as a function of temperature.

Figure 3.1. Thermodynamic interaction effects of a filler on diffusive
transport.

Figure 3.2. Hollow fiber membrane permeation cell.

. Figure 3.3. Correlation between distribution ratio and solubility
parameter for substances in a silicone elastomer membrane at 25 °C.

Figure 3.4. Correlation between diffusivity, corrected for tortuosity,
and the molar volume for substances in a silicone elastomer membrane
at 25 °C.

Figure 3.5. Correlation between surface free energy,
[RT/(N1/30vi2/3)]°[ln(k'i) - ln(Vf/Vp)], and cohesive energy density, 812,
for substances in a silicone elastomer membrane, at 25 °C. The line is
fitted to the halogenated compound and alcohol data only.

ix

Figure 3.6. Correlation between experimental and theoretical
selectivities for substances relative to methane in a silicone elastomer
at 25 °C.

Figure 3.7 . Correlation between experimental and theoretical

selectivities for substances relative to methanol in a silicone elastomer
at 25 °C.

Figure 4.1. The effect of temperature on the stationary phase/mobile
phase distribution ratio, Ki, obtained by ME (a) and by GC (b).

Figure 4.2. The correlation of the distribution ratio, K,, with boiling
point, T1”, at 25 °C. obtained by ME (a) and by GC (b).

Figure 4.3. The effect of temperature on diffusivity, DLS, in the ME
stationary phase.

Figure 4.4. The correlation of diffusivity, DLS, with boiling point, Tm,
at 25 °C. obtained by ME (a) and by GC (b).

Figure 4.5. The effect of temperature on permeability, P1, in the ME
stationary phase.

Figure 4.6. The correlation of the enrichment factor (over nitrogen),
81 /N2' with boiling point, Tm, for the data obtained by ME at 25 °C.

Figure 4.7. The correlation of GC retention times with ME permeation
parameters at 25 °C.

Figure 5.1. Flow-over hollow fiber membrane extractor.
Figure 5.2. Flow-through hollow fiber membrane configuration.

Figure 5.3. A cross-section view of the effect of boundary layers on the
permeation process.

Figure 5.4. Response for toluene vs. sample flow rate through a 2.5-
cm-long, 0.0305-cm i.d., 0.0635-cm o.d. hollow fiber.

Figure 5.5. The response curves for m/z 92 following a step change in
the concentration of toluene in a gas sample with different lengths of
ME—MS interface tube lengths.

Figure 5.6. Response time vs. ME-MS interface tube length for various
volatile compounds.

Figure 5.7. The response curves for l-butanol (m/z 56) with different
lengths of ME-MS interface tube.

X

Figure 5.8. Comparison of response vs. concentration plots for the
flow-over and the flow-through membrane extractor configurations.

Figure 5.9. Relative organic/water response ratios for the flow-over vs.
flow-through inlets obtained at comparable sample linear velocities.

Figure 5.10. Exploded view of the hollow fiber membrane extractor
valve.

- Figure 5.11. Exploded view of the sheet membrane extractor valve.

Figure 5.12. A membrane extraction valve coupled to a direct
insertion probe.

Figure 5. 13. A configuration of ME valve where the lower section of
the valve is expanded so that the process is carried out in direct
contact with the membrane.

Figure 6.1. A configuration for the influent and efiluent analysis by
ME-MS of a multi-stream, multi-phase process.

Figure 6.2. A diagram of the wastewater treatment bioreactor.

Figure 6.3. The syringe and mixing jar configuration for spiking
organic compounds into liquid streams.

Figure 6.4. A process flow diagram illustrating the spiking and on-line
sampling of three wastewater treatment bioreactors.

. Figure 6.5. Mass flow rate plots for carbon tetrachloride in A, reactor
3 (reactive, not spiked), B, reactor 2 (non-reactive, spiked), and C,
reactor 1 (reactive, spiked). The spike was begun at the 8-hour mark.
Figure 6.6. Mass flow rate plots for benzene in A, reactor 3 (reactive,
not spiked), B, reactor 2 (non-reactive, spiked), and C, reactor 1
(reactive, spiked). The spike was begun at the 8-hour mark.

Figure A.l. Experimental determination of permeation parameters.

xi

CHAPTER 1

Introduction

 

The need for real-time trace analysis of air and water streams
has increased in recent years. Methods are being sought for on-line
analysis of process streams for process optimization and control. The
challenge of environmental monitoring of air and wastewater
emissions grows with increasingly stringent government regulations.
In many cases, the extraction, concentration, desorption, and analysis
of organic compounds from air or water streams can be accomplished

in a single step using a membrane extraction device.

BACKGROUND

Membranes have long been used in industry and medicine for
processes requiring purification or enrichment of a gas or liquid
stream (1, 2). These membrane processes include separation of
hydrocarbons, separation of the components of air, purification of
water, and detoxification of blood. The same membranes used in
these industrial and medical processes also may be utilized on a
smaller scale in analytical separations. Terms that are commonly used
by membrane technologists (3) and the analogous terms that may be
used by analytical chemists are summarized in Table 1.1. These terms
may be used interchangeably in this work.

1

Table 1. l. Membrane separation terms and some analogous terms

used in analytical chemistry.

membrane technology term

membrane
feed
reject

permeate
permselectivity

diffusivity

permeability
solubility

alternate terms

stationary phase

sample stream, mobile phase
waste stream, vent stream

extract stream
enrichment factor, concentration
factor

diffusion coefficient

permeation coefficient
Henry's law coefficient,
distribution ratio

In general, membrane processes are comprised of the

membrane, the feed stream (sample), the reject stream (waste or

vent), and the permeate stream (sample extract) as shown in Figure

1.1. The permeate stream is enriched in analytes due to the selective

permeation properties of the membrane. The permeation of an

analyte through a membrane is defined by three processes;

1) selective partitioning of the analyte from the sample into the

membrane polymer matrix,

2) selective diffusion of the analyte through the membrane, and

3) desorption of the analyte from the membrane into a vacuum or

sweep gas.

Diffusion through the membrane is assumed to be the rate

determining process, while partitioning at the sample surface and

desorption from the permeate surface are considered to be

reject
(waste)

 

permeate
(extract)

_>

membrane

 

feed
(sample)

Figure l. 1. The components of a typical membrane extractor.

 

\\‘\‘\\\\\‘\\\\\\\\‘\\\\\\\‘ t-‘——u—‘—————-

steady state

 

non-steady state

   

NORMALIZED AMOWT

IIIIJII'I'IIIIIIIIIIIIII’IIIIIIIII,

 

 

 

H’ TIME

feed concentration
— permeation rate

Figure 1.2. A typical membrane permeation response curve.

instantaneous. A step change in analyte concentration in the sample
results in the typical permeation response curve shown in Figure 1.2.
The sensitivity of a membrane separation technique is determined by
the steady state permeation response, while the non-steady state
permeation characteristics of the analyte in the membrane determine
the response time. These processes will be discussed in detail in the

following chapters.

The development of membrane extraction (ME) techniques
have given birth to a family of powerful hyphenated analytical
techniques, including ME—mass spectrometry (ME-MS) (4, 5), ME-gas
chromatography (ME-GC) (6), ME-flow injection analysis (ME-FIA) (7),
ME-liquid chromatography (8), ME-ion chromatography (9), and
others, including GC-ME-MS (10, 1 1) and FlA—ME-MS (12, 13). The
membrane extractor is much more than an inlet or sampling system
for an analyzer. Membrane extractors have become indispensable for
techniques that require high specificity, sensitivity, and speed,

particularly for on-line analyses (14- 16).

Although applicable to any analytical technique, the membrane
studies and applications described in this work were performed with
analyses of the permeate by mass spectrometry. Historically,
membranes have been used as molecular separators in gas
chromatography-mass spectrometry (GC-MS) to reduce the amount of
helium carrier gas flowing into the mass spectrometer. Llewellen and
Littlejohn (10) have used a flat silicone membrane that is selectively

permeable to organic molecules relative to helium. The GC effluent

flows across one surface of the membrane, through which the organic
molecules permeate into the analyzer while the helium is largely
rejected. Lipsky, Horvath, and McMurray (1 1) used a heated Teflon
tube to act as a molecular separator interface for GC-MS. In this case,
helium preferentially permeates the porous Teflon membrane,
resulting in an enrichment of the organic analytes flowing into the

analyzer as the stream rejected by the membrane.

Westover, Tou, and Mark (5) evaluated various hollow fiber
membrane materials for MS analysis of organic compounds in air and
water without GC separations. The membrane was the direct interface
between the sample and the analyzer, with the inside of the hollow
fiber exposed to the MS vacuum and the outer surface exposed to the
sample. This particular configuration will hereafter be termed the
"flow-over" hollow fiber inlet. Cooks and co-workers (17) reversed the
configuration such that sample flows through the inner volume of the
hollow fiber while the outer surface is exposed to the MS vacuum.
Hence, "flow-through" will be the terminologr describing this
configuration. The two configurations are contrasted and discussed in
detail in Chapter 5. Except where specifically stated, all of the data
reported in the present work were obtained with a flow-through
hollow fiber membrane extractor. There are advantages to analyzing
the sample directly without chromatographic separation. In cases
where interferences between analytes are minimal or can be
accounted for, the analysis or screening of batch samples can be
shortened (12). In addition, transient processes can be much better

studied by direct and continuous analysis (18, 19).

GOALS OF THIS WORK

Much of the literature on the subject of sampling with
membranes is devoted to useful applications. Relatively little emphasis
has been placed on the development of practical models (a) for
predicting the capacity of a membrane to separate two components in
a sample or (b) for choosing the appropriate material for performing a
desired membrane separation. A goal of the present work was to
provide useful models and experimental guidelines for performing
membrane extractions so that the versatility of the technique may be
better exploited.

In Chapter 2, generalized forms of the permeation rate
equation for analytical applications to both air and water samples are
developed. Results and discussion of the effects of various
experimental parameters on permeation rates are presented with
their theoretical bases. A mass spectrometric method for determining
the permeation parameters, including enrichment factors,
permeabilities, diffusivities, and distribution ratios, will be presented.
Many of the results in this chapter have been published (20, 21).

In Chapter 3, a permeation model is developed based on
regular solution theory. Equilibrium partitioning of substances
between the membrane and feed phases results in two phases that
may modeled utilizing Hildebrand solubility parameters. In addition,
the effect on diffusive transport of partitioning a diffusing substance

between a filler and polymer phase in a composite membrane also may

be correlated to solubility parameters. Finally, experimental and
theoretical enrichment factors for a composite membrane are
correlated in the solution-diffusion model. The information presented

in this chapter has been published (22).

Chapter 4 is a practical extension of the principles developed
in Chapter 3. In Chapter 4, chromatographic separation principles
and data are applied to membrane extractions. Since both techniques
are governed by the same thermodynamic and kinetic factors, a model
is described utilizing well known chromatographic principles. Very
good experimental agreement is observed in correlations made
between the selectivities obtained by membrane extractions and by gas
chromatography. Such correlations become more complicated for
strong hydrogen bonding compounds because the membrane contains
a finely dispersed silica filler to provide it with strength and elasticity.
This silica filler affects both the thermodynamic and the transport rate
properties of the material. Comparisons are made between a simple
boiling point model and the solubility parameter model described in
Chapter 3. The information presented in this chapter has been
submitted for publication (23).

In Chapter 5, guidelines for the construction and use of simple
membrane inlets are presented. Experimental parameters are
discussed in the context of analytical sensitivity and response time.
These experimental parameters include analyte concentration, sample
flow rate, temperature, membrane thickness and surface area,

membrane extractor configuration, and distance of the membrane

extractor from the analyzer and the sample. Portions of this chapter
have been previously published (20, 21). Much of the additional
information has been submitted for publication (24).

In Chapter 6, the application of an ME-MS technique that was
developed for on-line analysis of organic components of multiple liquid
and gas streams is presented. The silicone membranes are shown to
allow for extraction of organic chemicals from complex and dirty
matrices with no sample preparation. Multiple streams of both air and
water were analyzed on-line with a single analyzer. This method has
been applied in an aerobic biological wastewater treatment process.
Mass balance determinations were performed by quantitatively
measuring the organic contaminants in the influent wastewater
stream, in the effluent water stream, and in the effluent air stream.

The information presented in this chapter has been published (25).

REFERENCES

(l)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(ll)

(12)

Bier, M., Ed. Membrane Processes in Indusg and Biomedicine;
Plenum Press: New York, NY; 1971.

Hwang, S.-T.; Kammermeyer, K. Membranes in Separations;
Robert E. Krieger Publishing: Malabar, FL; 1984.

Gekas, V. Desalination 1988, 68, 77.

Hoch, G.; Kok, B. Arch. Biochern. Biophys. 1963, 101, 160.

Westover, L.B.; Tou, J. C.; Mark, J. H. Anal. Chem. 1974, 46, 568.

Bredeweg. R. A.; Langhorst, M. L.; Dittenhafer, D. R.; Strandjord,
A. J .; Willis, R. S. 16th Annual Meeting of the Federation of
Analytical Chemistry and Spectroscopy Societies, Chicago, IL,
1989.

Melcher, R. G. AnaL Chim Acta 1988, 214, 299.

Melcher, R. G.; Bouyoucos, S. A. Process Control and Quality
1990, 1, 63.

Stevens, T. S.; Jewett, G. L.; Bredeweg. R. A. AnaL Chem 1982,
54. 1206.

Llewellen, P. M.; Littlejohn, D. P. US. Patent 3,429,105,
February, 1969.

Lipsky, S. R.; Horvath, C. G.; McMurray, W. J. AnaL Chem. 1966,
38. 1585.

Langvardt, P. W.; Brzak, K. A.; Kastl, P. E. 34th ASMS Conference
on Mass Spectrometry and Allied Topics, Cincinnati, OH, 1986.

10

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

Hayward, M. J .; Kotiaho, T.; Lister, A. K.; Cooks, R. G.; Austin, G.
D.; Narayan, R.; Tsao, G. T. AnaL Chem. 1990, 62, 1798.

Kallos, G. J.; Tou, J. C. Environ. Sci. Technol. 1977, 11, 1101.

Heinzle, E.; Reuss, M. Mass Spectromem in

Biotechnological Process Analysis and Control; Plenum Press:
New York, NY; 1987.

Savickas, P. J.; LaPack, M. A.; Tou, J. C. AnaL Chem 1989, 61,
2332.

(a) Bier, M. E.; Cooks, R. G.; Tou, J. C.; Westover, L. B. U.S. Patent
4.791.292. 1989.
(b) Bier, M. E.; Cooks, R. G. Anal. Chem 1987, 59, 597.

Tou, J. C.; Westover, L. B.; Sonnabend, L. F. J. Phys. Chem
1974, 78, 1096.

Calvo K. C.; Weisenberger, L. B.; Anderson, L. B.; Klapper, M. H.
Anal. Chem 1981. 53. 981.

LaPack, M. A.; Tou, J. C.; Enke, C. G. 37th ASMS Conference on
Mass Spectrometry and Allied Topics, 1989, Miami Beach, FL.

LaPack, M. A.; Tou, J.C.; Enke, C.G. Anal. Chem 1990, 62, 1265.

LaPack, M. A.; Tou, J. C.; McGuffln, V.L.; Enke, C. G. J.
Membrane Sci. 1994, 86, 263.

LaPack, M. A.; Tou, J. C.; McGuffin, V.L.; Enke, C. G. Anal. Chem
submitted for publication.

LaPack, M. A.; Tou, J. C.; Cole, M. J.; Enke, C. G. Anal. Chem
submitted for publication.

LaPack, M.A.; Tou, J.C.; Enke, C. G. AnaL Chem 1991, 63, 1631.

ll

CHAPTER 2

Permeation Fundamentals

 

Permeation is a broad term that describes a variety of processes
involving transport of substances across boundaries (1). Many of these
processes have been given specific phenomenological names. For
example, as opposed to gas permeation, the term pervaporation is
often used to describe the penetration of a substance into a polymer
from the liquid phase, diffusion of the substance through the polymer,
and desorption from the polymer into the gas phase (2, 3). It has
been suggested that the term sorption indicates the penetration into
the polymer of a substance from the gas phase while absorption
indicates the penetration from the liquid phase (4). Regarding the
work described in the following pages, the more broadly descriptive
terms, permeation and sorption, will be used in both gas and liquid
applications. The term adsorption will be used in describing the
assimilation of molecules from a gas or liquid phase by an impermeable
surface. The term desorption describes the reverse process of

sorption, absorption, and adsorption.

As introduced in Chapter 1, the permeation of a compound
through an amorphous polymer is governed by sorption of the
compound into the polymer, diffusive transport through the polymer
matrix, and desorption from the downstream side of the polymer.

12

This description of the permeation process is generally known as the
solution-diffusion model (5). Sorption and desorption are equilibrium
processes that may be described by classical thermodynamics (6, 7) as
will be discussed further in Chapters 3 and 4. Because it is such a
rapid process, desorption of the permeating compound into a vacuum
or carrier gas is commonly ignored when discussing the permeation of
gases and volatile organic compounds. The diffusion process is driven
by the concentration gradient across the thickness of the membrane.
Quantitative treatments of diffusion in solids under various conditions
have been presented (8, 9). In this chapter, sorption and diffusion are
discussed in regards to the two regions of the permeation rate curve,
steady state and non-steady state (see Figure 1.2), and to their
importance to the selectivity of the permeation process.

STEADY STATE PEWTION

Steady state permeation is described by Fick's first law

F1: -A-D1,S-8c1.s/ax (2.1)

where F1 is the flow rate (permeation rate) of substance i in the

permeate (extract stream), A is the surface area of the membrane, Di,s

is the diffusivity of the substance in the membrane polymer (stationary

phase), and acts/ax is the concentration gradient for substance 1

across the membrane thickness. For a sheet membrane, Fick's first

law gives

13

F1 = A‘Dr,s'(Cr,sl ' Ci,52)/d (2.2)

and for a hollow fiber membrane,

F1 = 2.“.L.DI,S.(CI.SI - Ci.sz)/1n(0.d./I.d.) (2.3)

where cle and c152 are the concentrations of substance i in the feed

surface and the permeate surface of the membrane, respectively, d is
the thickness of the sheet membrane, L is the length of the hollow
fiber, and o.d. and i.d. are the outer and inner radii of the hollow fiber,
respectively. The general components of the permeation process are
shown in Figure 2.1 (for a sheet membrane). If the permeate side of

the membrane is exposed to the mass spectrometer vacuum or swept

with a carrier gas, a concentration gradient is established and c521

becomes very small relative to Ci,s1 and can be ignored. This

concentration gradient is the driving force for diffusion. The
concentration c151 is established by the partitioning process and, for

gas samples, is directly proportional to the partial pressure of
component i, p1, in the sample by the Henry's law of solubility

coefficient, Si, such that 01.31 = Sl-pi. However, since the desired

measurement for most analytical methods is concentration and not
partial pressure of a substance in the sample, Equations 2.2 and 2.3

can be rewritten for the sheet as

Fr = A'Dr,s'SI'Pt’(Pr/Pt)/d (2 - 4)

and for the hollow fiber as

14

Permeation through a Membrane

1) Sorption into the membrane
2) Diffusion through the membrane
3) Desorption from the membrane

membrane

sienna ._ .. ._...ha_$_9‘

      

if »

sample or feed stream
(mobile phase)

 

Cm

 

extract or
permeate stream

 

F = A-Ds-K-cm/d

A
V

 

Figure 2.1. A cross-section view of the general components of the
permeation process.

15

F1 = 2.1'C°L°D1,S'Si’pt°(pi/pt)/ln(O.CI./I.d.) . (2 . 5)

The substance i partial pressure/ total sample pressure ratio,

pi/pt, gives the molar concentration of the substance in the feed
(mobile phase), ch. The product, Si-pt, can be rewritten to yield the
ratio of the concentration in the membrane, 01.31, to the concentration
in the feed, chm, which is defined as the concentration distribution

ratio, where Ki = CLSI/ctm. The distribution ratio provides a more

generalized form of the permeation rate equation, where for the sheet

F1 = A.DI,S.KI.Ci,m/d (2 . 6)

and for the hollow fiber

F1: 201r-L0D1,SOK100LS/ln(o.d./i.d.) (2.7)

This form of the permeation rate equation is also readily applied
to aqueous samples where the membrane/water distribution ratio for
the substance and the concentration of the substance in the aqueous

sample are used (10). The product of diffusivity and distribution ratio
is the permeability (Pi = DLSOKi). Typically, membrane technologists

utilize the Henry's Law coefficient (Pi = Dr,s'Si) and the units
cm3-cm/[s-cm2-cm-Hg] for gas permeabilities. Since the distribution

ratio has no units, the units for permeability will be given as

cm2/[svciml where appropriate in the present work.

16

At a given temperature and pressure, the permeability and the

dimension factor (A/d for the sheet, 2 1r L/ln(o.d./i.d.) for the hollow

fiber) are constants. The permeation rate and therefore the analytical

signal, 1,, is directly proportional to the sample concentration, where

11 = Qr'Fr = l'fr'Crm (2-8)

where Q. is the absolute instrumental response factor and rfi is the

analytical response factor for compound i. Depending upon the
application, the sample concentration may, in fact, be expressed in
any useful units to obtain an analytical working curve. For example,
organic contaminants in aqueous samples are often expressed in units
of mg/ L, while organic contaminants in air may be expressed in units

of L/ L or mole/ mole.

The linear relationship between permeation rate and sample
concentration is exhibited over a wide dynamic range, as shown in
Figure 2.2, in which the response is directly proportional to the
permeation rate. The upper limit of this range is determined by the
maximum amount of analyte that the analyzer will tolerate for linear
response and/ or the swelling of the membrane due to high sorption of
organic analytes. Aqueous samples generally provide a wider dynamic
range because the low end of the range is extended. The detection

limits for aqueous samples are generally lower than for air samples.

17

     
   

 

 

 

 

10000 "
E
g 1000 ‘* toluene
E‘ in water
5 100 ~-
E toluene
v 10 r- in air
0
m
s 1...
O.
in
:16
0.1 i l i
7 l
g 6 toluene
: t 5» hrak
m o
m u 4
2 h
a C3 3
g - 2 toluene
1 In water /‘
0 , i l

 

 

1 1 00 10000 1 000000

Concentration, ppb

Figure 2.2. The mass spectrometric response and pressure vs.
concentration of toluene in the feed stream. Aqueous standard
concentrations are reported on a grams/liter basis while gas
standards are reported on a volume [volume basis. The portion of the
toluene in air response curve labeled ¥ deviates from linearity due to
excessive pressure in the ion source.

18

Effects of membrane dimensions

It is apparent from Equations 2.6 and 2.7 that increasing the
surface area of the sheet and the length of the hollow fiber
proportionally increases the permeation rate. Membrane thickness
has an inverse effect on permeation. For a sheet membrane, the
permeation rate is simply proportional to l /d. For a given length of
hollow fiber, the effect of hollow fiber radial dimensions on
permeation is given by l /ln(rO/r1). A comparison of signals obtained
from the analysis of organic compounds in air with two hollow fibers of
approximately equal lengths, but different radial dimensions, is shown
in Table 2.1. Experimental and theoretical response ratios show
reasonably good agreement for individual components as well as for

the total gas throughput indicated by the analyzer pressure.

Table 2. 1 . Efiect of hollow fiber membrane radial dimensions on
analytical response. The silicone hollow fibers were 2.5-cm long.
Temperature :- 23 °C.

response, (arbitrary units)

 

 

 

membrane 1 membrane 2 response

i.d.=0.0305 cm i.d.=0.147 cm ratio, I1/12
compound o.d.=0.0635 cm o.d.=0.l96 cm e_xp_._ theor.
dichloromethane 2.8 5.5 2.0 2.5
1 , 1 -dichloroethene 0.6 1.3 2.2 2.5
chlorobenzene 1 .2 2.4 2.0 2.5
acetone 0.8 2.0 2.5 2.5
analyzer pressure 6.2x10‘8 1.4x10'7 2.3 2.5

(torr)
analyzer base pressure = 2.0x10-9 torr.

19

Effects of temperature
Permeation is a temperature-dependent phenomenon obeying

the Arrhenius relation:

P1 = P1.0.Cxp['Epi'( 1 /RT' 1 /RT0)] (2. 9)

where the initial permeability of substance i, Pro, is given at some
initial temperature, To, the activation energy for permeation, Epi, is
the sum of the activation energy for diffusion, EDI, and the difference
in heats of solution between the membrane and the sample matrix,
AHSi = HS,(membrane)-H51(matrix) for substance 1. Substituting
Dr,s'Ki = P1 into Equation 2.9 gives

DI,S.KI = DI,SO.KI.O.exp[-(EDI + AHSI).(1/RT-1/R'r0)l (2 . 10)

The activation energy, Em, is greater than zero, while in

general, AHSi is less than zero. The direction for the change in

permeability with changing temperature is dependent upon whether

the change in diffusivity or distribution ratio dominates, as determined
by the relative magnitudes of ED, and AHSl.

The relative trends for the permeabilities of air, water, and
organic compounds with increasing temperature are shown in Figure
2.3. At higher temperatures, permeabilities of air and water increase

because increasing diffusivities dominate their permeability-
temperature relationship. Organic permeabilities from water samples

also increase largely due to increasing diffusivities. In contrast to

20

16

 

 

 

 

 

T
.42 14 .- ‘
C
a water
a 12 ur—
8
1:: 1o --
3
g 3 -- bromoform
: in water
0
9. 6 .—
O
I:
0 4 .- .
3 nitrogen
E; I (oxygen follows)
3 2 .- . 4
r: ._.

oi ~—e
0 g : bromo'iorm in air
20 40 60 80

Temperature, °C

Figure 2.3. The efi'ects of temperature on permeability.

21

Table 2.2. Survey of temperature efiects on detection limits (S/ N a
2) for organic compounds in air and water. The membrane is a 2.5-

cm long. 0.0305-cm i.d., 0.0635-cm o.d. silicone hollow fiber.

compound

chloromethane
dichloromethane
chloroform

carbon tetrachloride
chloroethene

1 , 1 -dichloroethene
trichloroethene
tetrachloroethene
dibromomethane
bromoform

benzene

toluene
ethylbenzene
chlorobenzene

l ,3-dichlorobenzene

1 ,2 , 4-trichlorobenzene

M
50
84
83

117
62
61

128

166

172

171
78
91

106

112

146

180

detection limit (ppb)

 

22

inair
26°C

325
669
182
130
269
101
30
29
28
14
42
31
45
12
3

3

45 °C

 

368
742
233
163
301
125
39
34
36
21
54
38
57
14
3

5

in water
M 51.11;
6 5
7 5
18 13
6 5
29 25
32 25
106 93
62 34
3 2
2 2
6 5
7
23 16
51 29

aqueous samples, air samples show a decrease in permeabilities for
organic compounds due to their reduced partitioning into the
membrane at higher temperatures. This effect will be discussed
further in the following chapters. Since, as shown in Table 2.2,
organic permeabilities decrease for air samples with increasing
temperatures, their detection limits increase. Because of the greater
permeabilities of organic compounds from water at higher
temperatures, their detection limits improve. However, organic
enrichments decay at higher temperatures, as discussed below.
Further observations on these temperature-related phenomena are
presented below in the discussion on organic enrichment and their

implications in chemical analyses are discussed in Chapter 5.

N ON -STEADY STATE PERMEATION

Non-steady state permeation is governed by Fick's second law:

aCLS/at = ‘DLS‘(82CLS/aX2). (2 . 1 1)

The mathematical solution for diffusion through a membrane of

thickness (1 following a step change in sample concentration is (1 1)

Fi(t) = Fussfll + [2021-1)“0exp(-(n01r/d)2 Dl,s°t)1}- (2.12)

Where Fifi) and Fuss) indicate the permeation rate of substance i at time

t and at steady state conditions, respectively. The permeation process

exhibits an asymptotic approach to steady state, thus the time

23

required to achieve steady state, or even 95% steady state, t95, may be

difficult to determine. It is convenient, therefore, to relate response

time to the time required to achieve 50% steady state permeation, t50,

which is more easily determined. The first order approximation at
t50, neglecting all but the first exponential term (n=l), can be used to

determine the diffusion coefficient (12), where

1),.s = 0.14-(d2/t50) (2.13)

Further evaluation yields a t95/t50 theoretical ratio of 2.7. Good
agreement is obtained for times greater than t50 when the first

approximation is applied to experimental response curves, as shown
in Figure 2.4. Thus, the response time approximation t95 = 2.7-t50 is
valid. For times less than t50, additional terms in the polynomial are
required for a good fit. Response times are reported in this work in

terms of t5o measurements.

Effects of membrane dimensions
Since diffusivity is a constant for a given substance in a given
polymer and at a given temperature, the response time-thickness

relationship can be expressed as follows:

t(50)2/t(50)1 = (dz/d1)2. (2.14)

The increase in response times for organic gases permeating a
hollow fiber membrane with a 0.0216-cm wall thickness compared
with that for a 0.0165-cm wall thickness is shown in Table 2.3. As

24

 

 

 

 

 

I so...
-- e

09 . I .
00.8 ""
" 85°C
Ir"0.7 4
r:
206 .. 26°C
a o
o
50.5
o
n.

0.4 --
a
3
:0.3 -- /
a
E
30.2 -r
z

0.1 -*

0 i i i i i i i i i i I; i i

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Time, minutes

Key:

Circles and squares = experimental data

Thin lines = solutions using only the first term (n=1) of the polynomial
Heavy lines = solutions using the first five terms (n=1-5)

Figure 2.4. A plot of solutions to non-steady state permeation
(Equation 2. 12), calculated from t5o values. and permeation

response data for chloroform at 26 °C and 85 °C.

25

described in the Appendix, the experimental measurement of t50 is

dependent upon errors in defining the steady state permeation
response and in establishing the time when the sample makes initial
contact with the membrane, to. Thinning of the membrane caused by
the pressure difference between the inside and the outside of the
hollow fiber also may result in the deviations between the
experimental and theoretical response time ratios in Table 2.3.

Table 2.3. Eflects of membrane thickness on response time for gas
phase organic compounds. The membranes are 2.5-cm long
silicone hollow fibers. Temperature = 23 °C.

response time (minutes) t(50)2/t(50)1

 

compound Q1 =0-0 1 65 cm mm e_xpg theor.
dichloromethane 0.38 0.60 1 .6 2 . 2
l , 1 -dichloroethene 0.28 0.48 1.7 2.2
chlorobenzene 0.72 1.60 2.2 2.2
acetone 1.88 3.02 1.6 2.2

Effects of temperature
Diffusivity obeys the Arrhenius relation given by

DI.S = DI,SO.exp[-EDI.(1/R’r- 1 /mo)]. (2.15)

Higher temperatures result in increased diffusivities and therefore
shorter response times. The permeation rate response curves for a

step change in sample concentration at various temperatures are

shown for 1,2,4-trichlorobenzene in Figure 2.5. The t50 values for

26

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Normalized Permeation Rate

0.2

0.1

1
I

   
 
 
   

26 °C

I

"‘6! :_

‘9 c o
‘ {‘2’93

    

 

 

I i I I i l I
I l I I I I

0 5 1 0 1 5 20 25 30 35 40

Time, minutes

Figure 2.5. Normalized permeation response curves for 1 ,2,4-
trlchlorobenzene as a function of temperature.

27

Table 2.4. Survey of temperature efiects on response time, t50, for

organic compounds in nitrogen. The membrane is a 2.5-cm long,
0.0305—cm i.d., 0.0635-cm o.d. silicone hollow fiber.

compound

chloromethane
dichloromethane
chloroform

carbon tetrachloride
chloroethene

l, l -dichloroethene
trichloroethene
tetrachloroethene
dibromomethane
bromoform

benzene

toluene
ethylbenzene
chlorobenzene

1 ,3-dichlorobenzene

1,2,4-trichlorobenzene

response time, t50, (minutes)

 

26 °C

0.23
0.34
0.42
0.52
0.25
0.36
0.41
0.78
0.57
1.30
0.43
0.59
0.86
0.93
4.40
8.70

45 °C

0.19
0.30
0.36
0.38
0.20
0.30
0.35
0.55
0.40
0.88
0.32
0.46
0.60
0.63
1.70
4.60

65 °C

0.18
0.24
0.30
0.32
0.18
0.25
0.28
0.41
0.33
0.62
0.26
0.35
0.42
0.45
1.00
3.00

85 °C

0.17
0.20
0.24
0.27
0.16
0.23
0.21
0.33
0.25
0.50
0.24
0.24
0.30
0.37
0.95
2.00

several gas phase organic compounds at different temperatures are
given in Table 2.4. Aqueous sample response times mimic gas samples
when the transport-rate through the sample is negligible, as discussed
in detail in Chapter 5.

ORGANIC ENRICHMENT

The relative permeability through the membrane for one
compound over another determines membrane selectivity. The
enrichment factor, 81/], of one component, i, over another, j, (e.g., an
organic compound over the sample matrix) is defined by the ratio of
their permeabilities;

81/] = (D1,S'K))/(DJ,S'KJI = (F1/C1.m)/(Fj/Cj.m) (2- 15)

Effects of membrane dimensions

The enrichment factor is independent of membrane
dimensions, as seen in Equation 2.15. Increasing the length or
number of the hollow fiber will increase permeation rates of all
components proportionally, with no effect on observed organic
enrichment, if Cmi does not change over the length of the hollow fiber.
Typically, increasing the membrane surface area will be more
efficiently accomplished by increasing the number, rather than the
length, of hollow fibers exposed to the sample.

29

Effects of temperature

With increasing temperature, the enrichment factors for organic
components are reduced because the permeabilities for air and water
increase more than the permeabilities for most organic compounds
studied, as shown in Figure 2.3. For trace level organic samples, the

analyzer pressure follows the permeabilities of the air or water.

Based on steady state response data used to determine the
detection limits in Table 2.2, permeabilities from aqueous samples
increased an average 35% (range = 14-83%) when the temperature
was increased from 26 °C to 45 °C for the compounds analyzed in
water. Diffusivities through the membrane for these same organic

compounds increased an average 46% (range = 13-159%) based upon

the response time data in Table 2.4, where [DS(45 °)-Ds(26 °)]/Ds(26 °)
= [l/t5o(45 °)-1/t50(26 °)]/[1/t50(26 °)]. Although the organic
permeabilities increased, water permeability increased 130% for the

same temperature change.

For air samples, organic responses decreased an average 20%
(range = 10—33%) when the temperature was increased from 26 °C to
45 °C. even though diffusivities increased an average 43% (range = 13-
159%). Therefore, the decrease in the membrane/ air distribution
ratio dominates the permeabilities for these compounds. While the
organic permeabilities decreased, the nitrogen permeability increased
29%. Enrichment factors relative to nitrogen and water for several

organic compounds are given in Table 2.5.

Table 2.5. Survey of temperature efi'ects on the enrichment over

the sample matrix for organic compounds in nitrogen and water.

compound

chloromethane
dichloromethane
chloroform

carbon tetrachloride
chloroethene

l , 1 -dichloroethene
trichloroethene
tetrachloroethene
dibromomethane
bromoform

benzene

toluene
ethylbenzene
chlorobenzene

1 , 3-dichlorobenzene

1 , 2,4-trichlorobenzene

enrichment factor

 

26$;
40
48
91
110
37
57
140
310
84
320
170
380
450
550
520
780

31

relative to nitrogen

4_5°_C_
27
33
58
74
26
35
81
180
50
170
1 10
230
280
330
350
400

relative to water

26°C

1900
2 100
1800

3300
970
600
190
570

2600

2300

2200

1300
470
450

45°C
1 100
1 100
1100

1800
530
360
100
330

1400

1300

1200
730
300
390

Most of the permeation parameters (permeability, diffusivity,
solubility, and enrichment factors) reported in the literature are for
simple gases such as hydrogen, nitrogen, oxygen, argon, and light
hydrocarbons and alcohols (15-20). Very few studies have been
performed to determine these parameters for the more complex
organic compounds that are of interest to analytical chemists (21, 22).
A mass spectrometric technique developed for obtaining the

permeation parameters reported in this work is described in the

Appendix.

32

REFERENCES

(l)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Hwang, S.-T.; Karnmermeyer, K. Membranes in Separations,
Robert E. Krieger Publishing Co., Inc.; Malabar, FL; 1984.

Frennesson, I.; Tragardh, G.; Hahn-Hagerdal, B. Chem Eng.
Commun. 1986, 45, 277.

Mulder, M. H. V.; Smolders, C. A. J. Membrane Sci. 1984, 17,
289.

Conway, B. E. In The Solid-Gas Interface, Vol. 2, Flood, E. A., ed.;
Marcel Dekker, Inc.: New York, NY; 1967.

Mears, P. In Membrane Separation Processes; Mears, P., Ed.;
Elsevier: Amsterdam, Netherlands; 1976.

Ben-Naim, A. Solvation Thermodmamics; Plenum Press: New
York, NY; 1987.

Karger, B. L.; Snyder, L. R.; Horvath, C. An Introduction
to Separation Science; Wiley-Interscience: New York, NY; 1973.

Barrer, R. M. Diffusion in and Throqu Solids; Cambridge
University Press: New York, NY; 1951.

Crank, J. The Mathematics of Diffusion, 2nd Ed.; Oxford
University Press: New York, NY; 1975.

Lee, C. H. J. App. Polym Sci. 1975, 19, 83.

Pasternak, R. A.; Schirnscheirner, J. F.; Heller, J. J. Polym Sci.
1970. 8. 467.

Ziegel, K. D.; Frensdorff, H. K.; Blair, D. E. J. Polym Sci. 1969,
7. 809.

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

Bier, M. E.; Kotiaho, T.; Cooks, R. G. Anal. Chem Acta 1990,
231. 175.

Lauritsen, F. R. Int. J. Mass Spectrom Ion Proc. 1990, 95, 259.

Stern, S. A.; Shah, V. M.; Hardy, B. J. J. Polymer Sci: Part B:
Polymer Physics 1987, 25, 1263.

Kammermeyer, K. Ind. Eng. Chem 1957, 49, 1685.

Hodgson, M. E. Filtr. and Separ. 1973, July/August, 418.

Kim, T. H.; Koros, W. J.; O'Brien, K. C. J. Membrane Sci. 1988,
37. 45.

Friedlander, H. Z.; Litz, L. M. In Membrane Processes in
Indust_r;y and Biomedicine, Bier, M., Ed.; Plenum Press: New
York, NY; 1971.

Bell, C.-M.; Gemer, F. J.; Strathman, H. J. Membrane Sci. 1988.
36. 315.

Ho, J. S.-Y.; Schlecht, P. C. Am Ind. Hyg. Assoc. J. 1981, 42, 70.

Ton, J. C.; Rulf, D. C.; DeLassus, P. T. Anal. Chem 1990, 62, 592.

CHAPTER 3

The Correlation of Permeability
with Hildebrand Solubility Parameters

 

In addition to guiding the selection of liquid extraction solvents,
the "like-dissolves-like" rule is commonly used to guide the selection
of membrane materials. For example, the extraction of non polar
organic compounds from an aqueous matrix can be accomplished with
a silicone membrane because of the tremendous selectivity this
polymer exhibits for the permeation of the non polar materials (Table
2.5). However, this simple rule does not predict nor explain the fact
that, in the gas phase, l-propanol permeates this same silicone
membrane nearly two times better than pentane and methanol
permeates over forty times better than methane. In addition,
membrane extractions are kinetic, as well as thermodynamic,
processes such that the effects of selective diffusivities in the
membrane become important, not only for the separation efficiency,

but also for the analytical response time.

A fundamental understanding of the membrane extraction
process, facilitated by a simple model, can help to generate more
versatile separation techniques and perhaps a wider selection of
membrane materials. In this chapter, a permeation model is

developed based upon Hildebrand solubility parameters. A correlation

35

of this model is made to the partition selectivity, to the diffusion
selectivity, and to the permselectivity or enrichment factor.

THE SOLUBILITY PARAMETER

As discussed in Chapter 2, the solution-diffusion permeation
model assumes that a permeating substance is in equilibrium at the
interface between the feed and membrane phases. This equilibrium,
in combination with a vacuum or sweep fluid at the permeate side of
the membrane, establishes a concentration gradient across the

membrane that results in diffusive flow. For component i, the

permeation coefficient, P1, is given by the product of the diffusivity,
DLS, and the Henry‘s law solubility coefficient, Si,

P1 = D1931 (3.1)

The permselectivity or enrichment factor, 81/], of a membrane for one

substance, i, relative to another, j, is defined as

81/] = (D1,s/Dj,s)'(SI/Sj) (32}

By assuming that the sorption of a gas into a polymer phase may
be modeled as a solution process, a correlation of solubility parameters
to the solution-diffusion permeation model arises naturally.

Hildebrand solubility parameters have been used in estimating the
compatibility of polymers with solvents, additives, and coatings (1-6).

36

The solubility parameter, 51, (7, 8) for substance i is the square root of

the cohesive energy density for the pure liquid substance, defined as

51 = IAEVI/Vill/2 = [(AHerTl/Vill/Z (3.3)

where AEVi is the molar energy of vaporization, vi is the molar volume,
AHVi is the molar heat of vaporization, R is the gas constant and T is

the absolute temperature. The relationship between the solubility

parameter and the activity coefficient, 71’s, for some substance i in

some phase m is given by the Flory-Huggins relationship (5)

lnlyi'sl = lnlvilvsl + (1 - [vi/vsDocDS + xLSO<I>52 (3.4)

where vS and (1)8 are the molar volume and the volume fraction of the

phase m, respectively, and the binary interaction parameter, acts, is

Xi,s = [vi/(R0145) - 8512 (3.5)

Application of the solubility parameter to separation processes
has been most successful for solutions of similar materials where
dispersion interaction forces predominate. The solubility parameter
theory has been expanded (1, 9) to include other interaction forces
such as dipole induction and orientation forces as well as hydrogen-
bonding forces. In the present study, the single parameter treatment
was found to give reasonably good correlations with experimental
results for a membrane composed of poly(dimethylsiloxane) with a

fumed-silica filler.

37

DEVELOPMENT OF THE MODEL

For the model described below, the following assumptions are
made:
1) The feed or mobile phase is an ideal gas.
2) The permeating substance is at infinite dilution in both mobile
(feed) and stationary (membrane) phases.
3) The distribution process can be described using the regular
solution model as modified by Flory-Huggins [5], with all assumptions
inherent therein. Specifically, no changes in phase volumes occur due
to sorption.
4) The diffusion process obeys Fick's laws, with all assumptions

inherent therein.

Distribution equilibrium
In the solution-diffusion model, an equilibrium is established at
the feed-membrane interface for a permeating substance as described

by Henry's law:

Xi,s = Pr/[Pro'Yrs] (3.6)

where Xl's is the mole fraction and 71’s is the activity coefficient of
substance i in the membrane stationary phase, 3, and p1 and p10 are
the equilibrium and standard-state partial pressures, respectively, for
the substance in the mobile phase. Equation 3.6 may be expressed in
the natural logarithmic form and combined with Equation 3.4 and

Equation 3.5 to yield

38

1n[X1,sl = 1nlp1/p1°l - lnlvl/vsl - (1 - [vi/vsl)°¢s
‘ [Vi/(m)].[81 ' 8512.¢52 (3-7)

In the case of a membrane consisting of two distinct phases, such as a
polymer with a uniformly distributed filler, the molar volume is
defined by

vs = vp-Xpfi + Vi‘st (3.8)

where VI) and Vf are the molar volumes and where Xp.s and Xfis are the
mole fractions of the polymer and the filler, respectively, in the
stationary phase. These parameters need not be quantitatively
specified in the treatment described below. Transport properties for
a substance in a polymeric membrane containing a filler have also been
modeled using the additive properties of the two phases in the
membrane (10, 1 1). Similarly, the solubility parameter for the

stationary phase based on regular solution theory is given by

as = tsp-cpl, + are, (3.9)

where 8p and 8f are the solubility parameters for the polymer and filler

phases, respectively, and (DP and (bf are the volume fractions of the

polymer and the filler, respectively, in the membrane. Equation 3.7 is

rearranged to give

IUIX1,S'IV1/Vsll = 1nIP1/P101 ' (1 ' [Vi/VSII'q’s
- [vi/(RT)]°[51 - 53]20<I>52 (3. 10)

39

At infinite dflution, X13 = nLS/ns, where the ratio Hrs/11s is the number

of moles of sorbed substance 1 per mole of stationary phase. Therefore,

the volumetric concentration of the substance in the stationary phase,

01.8, is given by

XI,S.[vI/VS] = VI,S/VS = CLS (3.1 1)

where Vr,s/Vs is the volume of the sorbed substance per unit volume of

stationary phase. Similarly, the volumetric concentration of the
substance in the gaseous mobile phase, Chm, is given by the ratio of the

partial pressure to total feed pressure:

Pi/Pt = Vi,m/Vm = Ci,m (3- 12)

Equation 3.10 can now be represented in terms of the concentration

distribution ratio, Ci,s/Ci,m = K1, where

lanil = lnlpt/pPl - (l - [vi/vsllflbs
- [v1/ (R’I‘ll-lfii - 5812-ch2 (3.13)

Because substance i is assumed to be at infinite dilution, (DS = 1.
In addition, the molar volume of the stationary phase, vs, is much

greater than that of the sorbed substance, v1. Therefore, Equation

3.13 reduces to

lanll = ln[pt/p1°] ‘ 1 ‘ [Vi/(m)].[81 ' 5512 (3-14)

This relationship is consistent with gas chromatographic studies of
dilute solutions of organic molecules in polymers (5). Hildebrand,
Prausnitz, and Scott proposed a model for the solubility of a gas in a
solvent in which the gas first condenses to a hypothetical pure liquid
and then dissolves in the solvent (8). In the case of non polar gases at
temperatures above their critical temperature, they have calculated
fugacities of these hypothetical liquids to estimate solubilities.
Solubility parameters have been calculated for such gases by Prausnitz
and Shair (12). Giddings, et. al (13) have described an expression for
determining the solubility parameters of compressed gases using their
critical properties. In the present work, an attempt is made to
develop a general model that provides predictions for the solubility of
gases of varying polarities and critical temperatures, using a minimum
of readily available parameters. This model utilizes the hypothetical
and experimental solubility parameter values provided in the
literature. In this model, the vapor pressure term in Equation 3.14 is
related to the Hildebrand solubility parameter by Equation 3.3 and the

Clausius-Clapeyron equation in the following manner:

lnlpt/plol = [v1/ (Rm-(51 - 002 (3.15)

The experimentally determined constant, (1, corresponds to the
solubility parameter for the hypothetical liquid feed matrix and
corrects for deviations from Henry's law, Flory-Huggins, and regular
solution theory. A correlation between the distribution ratio and
solubility parameter is then given by the following equation:

41

lan.) = lv./(RT)l-[(5. - 002 - (6, - 65)?) - 1 (3. 16)

The distribution selectivity for substance i relative to substance j

is calculated from

Kl/Kj = exp{[2°(55-a)°(51v1-51vj) + (0.2-852).(V1-Vj)]/(RT)} (3.17)

Diffusion
According to the free volume theory of Brandt (14), the
activation enery for diffusion, Em, in elastomers is dominated by

intermolecular forces and may be related to the cohesive emery

density of the polymer, 8P2, as well as dirmemsioms of the polymer

chains and diffusing substance. The relationship is given by (10):
Em = 0.5-spoop001-6p2-N (3.1 8)

where sp is the polymer segment length associated with the free

volume, op is the average diameter of the polymer molecule, a, is the

diameter of the diffusing substance, and N is Avogodro's number.
Equation 3.18 may be expressed in terms of the molar volume of the

diffusing substance:

Em = 0.620N2/ 3cspoop05p20v11/ 3 (3. 1 9)

Although the free volume of some liquids may be significant, for many
substances the liquid molar volume is consistent with the molecular

volume (7). For the purpose of the present model, the liquid molar

42

volume of the diffusing substance is used rather than the molecular
volume so that consistency with the solution model is maintained and

so that the number of variable terms are minimized.

The constants and polymer-related terms in Equation 3.19 may
be combined into a single constant parameter, 19, so that the activation
emery may be written to be proportional to the molar volume of the
diffusing substance. The dependence of the diffusivity on the molar

volume may then be described by
min”) = InID0,p1 - [fi/(RTll-v11/3 (3.20)

where r), the polymer-related constant, and lm[D0,p], the natural
logarithm of the diffusivity of some hypothetical substance with v=0,

are determined from the slope and the y-imtercept, respectively, of a
plot of ln[DLp] vs. v11/3.

Equation 3.20 does not account for the effects of a filler on
diffusive transport in a polymer. Thermodynamic partitioning or
adsorption of some substances may become significant in cases where
the two phases of the filled membrane are quite different in polarity or
hydrogen-bonding character. This inhibition of diffusive flow through
a filled membrane is manifested as an apparent diffusivity that is lower
than predicted from the molar volume of the substance. If it is
assumed that migration of a substance through the membrane occurs
only in the polymer phase, any delay in this migration time is due to
partition into or adsorption onto the filler. The individual retention

43

processes of this transport mechanism is illustrated in Figure 3.1.

The degree of retention by the filler in a composite membrane is

determined by the molar partition or adsorption coefficient, k'i,

k'l = an/nhp = “1,5 " tl,p)/ti,p (3.21)

where m” and “LP are the number of moles of substance i in the filler
and the polymer phases, respectively, at equilibrium, ti,p is the time
for diffusion of substance 1 through the polymer, and tr,s is the time for

diffusion of i through the filled membrane. Equation 3.21 may be

rearranged to give

tI,S = tl,p.(1 + k'l) (3.22)

It is clear from Equation 3.22 that no retention is observed when the
diffusing substance has no affinity for the filler (i.e., k'i = 0). The

diffusivity of substance i in the membrane may be deterrmined
experimentally from the sorption rate curves (15) using the following

equation:

1),: 0.14-d2/t(50) (3.23)

where d is the membrane thickness and t(50) is the time required to

attain one-half steady-state permeation following a step-change in the
concentration of the substance in the mobile phase. By combining
Equations 3.22 and 3.23, a relationship is obtained between the
diffusivities with and without retention by the filler:

44

FEED MEMBRANE PERMEATE

Polymer Phase
Filler Phase

   

»
Distribution ratio, K, \
established at \
membrane/feed interface ,\
& diffusive lo\

t Partition or adsorption \
Ii coefficient, k', established 1
\ at filler/polymer interface \
\ in membrane \

N\\\\\\\\\\\\\\\\\

 

 

Figure 3.1. Thermodynamic interaction efi'ects of a filler on
difl'usive transport.

01.3 = Dip/(1 + k'il (3.24)

where DLS is the diffusivity of substance i in the filled polymer
stationary phase and Di.p is the diffusivity in the unfilled polymer. This

relationship is consistent with that reported by Barrer and coworkers
(16, 17). In addition, a reduction in mass transport rates is observed
in a polymer containing impermeable particles or crystallites due to
the tortuous path the diffusing substance must travel (18). These
effects have been summarized by van Amerongen (19), where the
diffusivity in a membrane containing a non-retentive spherical filler is

related to that in the unfilled polymer by the volume fraction of the
filler in the membrane, (bf, such that:

BLS = Dl,p/[1 + “bf/2)] (3.25)

The retention and tortuosity terms are combined to yield the

diffusion-partition (D-k) model given by the following equation:

01.5 = Dip/{[1 + (of/mom + k',“ (3.26)

To estimate the diffusivity of a substance in a membrane that contains
a filler, Equations 3.20 and 3.26 are combined to give

Di.s = Do,p°exP{’[fi/(RT)]’V11/3}
/{[1 + (‘bf/le'll + k'fl} (3-27)

Whereas retention processes may play a large role, the tortuosity
factor is independent of the nature of the permeating substance and

is, therefore, not important for estimating selectivity.

Where retention arises from a thermodynamic partition process,
the distribution coefficient may be estimated using solubility
parameter theory. At equilibrium, if substance 1 is partitioned between
the polymer and filler phases, then

x1,f/ Xi,p = Yip/71f (3.28)

where the subscripts f and p designate the filler and polymer,
respectively. Rearranging and combining Equation 3.28 with
Equations 3.4 and 3.5 yields the following relation:

InIX.,f/Xi,pl = lnlvilvpl - lnlvllvfl + (l - [vi/VPD-wp
- (1 - [Vi/an"pf + [vi/(RTll-léi - 81,12“pr
- [Vi/(R'l‘n.[51 ' 5f]2.(bt2 (3.29)

Assuming infinite dilution for substance 1 in all phases and assuming
the molar volume of substance i to be small relative to the molar
volumes of the filler and polymer phases, Equation 3.29 is simplified
to the following:

1n[X1,f/X1,pl = 1n[(V1/ Vpll (Vi/Vii] + [V1/ (RT)]'[(51 - 5pm
- [Vi/(RT)1°[(81 - 5flzl (3.30)

47

Following the substitution of Equation 3.1 1 into Equation 3.30, the
distribution ratio for substance 1 partitioned between the filler and

polymer is given by

1n[C(,f/C(,pl = lan'il = [Vi/(RT)]°[(51 - 5pl2]
- [Vi/(RT)]°[(61 ' 5le] (3.31)

Since the distribution ratio is the product of the molar partition
coefficient and the volume phase ratio, K'i = k'1-(Vp/Vf), then Equation

3.31 can be rewritten as follows:

lnlk'il = lnivf/vp) + [vi/(RTH-[lfii - 8pm
- [v1/(RTn-u6, - 5,)2) (3.32)

If retention arises from an adsorption process, the entire
molecule may not participate in the interaction with the solid

adsorbent surface. The energy of adsorption at the surface is typically
described by the surface free energy, EN/ (Nl/ 3-v12/ 3), and involves

only the molar area, N1/30v12/3, of the adsorbed molecules (7, 20, 21).
Karger, Snyder, and Eon (9) have proposed a model of liquid-solid
chromatography in which the adsorption energr is proportional to the
product of the area of the adsorbed molecule and the cohesive energy

density. This relationship is given in the present model as

EA, = (RT)1n[K'1] = v12/3-[A-3,2 + B] (3.33)

where the proportionality constants, A and B, are determined
experimentally. The molar adsorption coefficient is correlated to the
Hildebrand solubility parameter and molar volume by the following

equation:

ln[k’1] = 1n[Vf/Vp] + [viz/3/(RT)]°[A0512 + B] (3.34)

This theoretical model may be compared with a model using a
modification of Equation 3.32 to describe adsorption of substances on
the filler phase. Since the entire molecule does not participate in the

adsorption process, the partial molar volume, v'i, of the surface-active

functional group may be substituted for the total molar volume, vi, in

Equation 3.32. In such cases, the molar adsorption coefficient may be

estimated as follows:

Inna.) = InIVf/vpl + [vi/(RT)1°[(6(- 5pm
- [v'i/(Rnlousl - 592) (3.35)

where V'f is the interfacial layer volume and V'f/Vp is the active volume

ratio, which is determined experimentally.

From Equation 3.27, the diffusion selectivity between substance i

and j is given by

Dis/DJ... = ((1 + k'jl/ll + k'(]}
- exP{-[13/(RT)]°[V)1/3 - vjl/31) (3.36)

49

where the molar adsorption coefficients, k'l and k'j, are obtained from

the experimental solutions for Equation 3.34 or Equation 3.35.

The distribution and diffusion-retention models have been
evaluated for a silicone elastomer membrane that contains a fumed-
silica filler. The experimental membrane separation parameters and

their correlations with the models are presented below.

CORRELATION OF DATA TO THE MODEL

Experimental conditions

The membrane used to investigate the correlation of solubility
parameters with permeability was a silicone elastomer, composed by
weight of 69% poly(dimethylsiloxane) and 31% fumed silica (0.011-
mm diameter particles). The membrane was a SilasticTM silicone
elastomer hollow fiber (2.5-cm length, 0.0305-cm i.d., 0.0635-cm o.d.)
from Dow Corning Corporation. The hollow fiber was mounted in a

stainless-steel tee as shown in Figure 3.2.

Gas-phase samples were prepared by injecting known amounts
of the substances of interest into a nitrogen-filled 5~L SaranTM gas
sampling bag (22, 23). The concentration of organic substances was
sufficiently low to prevent swelling of the membrane (less than 0.1%
by volume gas phase). The samples were analyzed immediately after
preparation to minimize sorption into the bag. The gas-phase samples
were pulled through the hollow fiber membrane at a rate of 100-

cm3 / minute with a gas pump from Metal Bellows Corporation.

50

 

Hollow Fiber

 

 

LAL““‘I1“‘1—V

 

 

  
 
  

 

““““““li

 

 

 

 

 

 

Membrane
Sealant “““““““ to Mass
............ E - Spectrometer
Per mea te

 

 

 

 

 

‘ ‘ ‘ ‘ ‘ ‘ “ ““‘ I

 

 

Feed

Figure 3.2. Hollow fiber membrane permeation cell.

51

Permeation measurements were obtained by mass spectrometry with a
Hewlett-Packard 5971-A Mass Selective Detector modified for process

analysis applications (24). All experiments were performed at 25 °C.

The membrane separation parameters including enrichment
factor, 8, permeability, P, diffusivity, D, and distribution ratio, K, were
determined for the substances of interest from mass spectral data in
combination with data from literature sources. The method for the
determination of these parameters is described in Chapter 2 and in
the Appendix of this work. The enrichment factor (81 /N2 = Pi/PN2)
values were determined from mass spectrometric response ratios and
molar response factors (25), as described previously (26). The

permeabilities were estimated from these experimentally determined

enrichment factors and a literature value for PN2 (26), where Pi =
81/N2(exp)0PN2(lit). The diffusivities were determined using Equation
3.23 and the permeation rate curves generated from the mass
spectrometric experiments (26). The distribution ratio, K1, in this

study replaces the Henry's law solubility coefficient (S = P1/ Di,s)

traditionally used in gas permeation studies. The distribution ratio of

the substance between the gaseous mobile phase and membrane

stationary phase is simply the product of Si and the total feed pressure
(26), where K1 = CLS/CLm = 81-76 cm Hg.

In order to provide a comprehensive test of the theoretical
models, a wide variety of substances with differing size and chemical
functionality was examined in this study. These substances include

permanent gases, alkanes, chlorinated and brominated hydrocarbons,

52

Table 3. 1 . Molar volumes (vi) and Hildebrand solubility parameters (5,)
from References 1, l2, and 28.

molar volume solubility parameter
compound m3 [mole (J [cm311/2
gases
nitrogen 32.4 5.3
oxygen 33.0 8.2
argon 57. 1 1 0. 9
carbon dioxide 55.0 1 2. 3
alkanes
methane 52. 0 1 1 .6
ethane 70.0 1 3. 5
propane 85.0 13.6
butane 1 0 l .4 1 3.9
pentane 116.2 14.3
hexane 131.6 14.9
heptane 147.4 15.1
aromatic hydrocarbons
benzene 89.4 1 8.8
toluene 1 06.8 1 8 . 2
ethylbenzene 1 23. 1 1 8.0
chloromethanes
chloromethane 55. 4 1 9.8
dichloromethane 63.9 1 9.8
chloroform 80.7 19.0
carbon tetrachloride 97. 1 1 7.6
chloroethenes
chloroethene 68. l 1 6.0
1,1 -dichloroethene 79.0 18.6
trichloroethene 90. 2 l 8.8
tetrachloroethene 10 1.1 19.0
bromomethanes
bromomethane 56. l 1 9 .6
dibromomethane 68.9 22.3
bromoform 87. 5 2 1.8
alcohols
methanol 40.7 29.7
ethanol 58.5 26.0
l-propanol 75.2 24.3
l-butanol 91.5 23.3

Table 3.2. mperimental permeation parameters for substances in a
silicone elastomer membrane at 25 °C.

compound PIXI 0516l DSIXI 0611’ SC
gases

nitrogen 0.028 2 1 0.00 1 3
oxygen 0.053 2 1 0.0025
argon 0.053 2 1 0.0025
carbon dioxide 0.33 l 3 0.026
alkanes

methane 0.13 1 6 0.0079
ethane 0.33 11 0.030
propane 0.80 6.4 0.1 3
butane 1.0 6.3 0. 1 6
pentane 6.9 4.5 1.5
hexane 8.8 3.5 2.5
heptane 2 2 3.2 7.0
aromatic hydrocarbons

benzene 1 3 4.9 2.8
toluene 2 7 3.5 7 .6
ethylbenzene 4 2 1 .7 2 5
chloromethanes

chloromethane 1.9 1 1 0.1 7
dichloromethane 9.7 9. 1 1.2
chloroform 1 2 4.9 2.4
carbon tetrachloride 1 2 2.9 4.2
chloroethenes

chloroethene 1.6 9.1 0.2 1
1, 1 -dichloroethene 8.0 5.8 1.4
trichloroethene l 8 3.7 4.8
tetrachloroethene 4 5 2.4 1 9
bromomethanes

bromomethane 1.9 9. 1 0.2 1
dibromomethane l 6 4.2 3.8
bromoform 6 7 1.3 5 2
alcohols

methanol 5.3 0.42 1 3
ethanol 1 1 0.40 28
1 -propanol 1 3 0.47 28
1-butanol l4 0. 50 29

0 Units for permeability are cm3(STP)°cm/[sscm2°cmHg]
b Units for diffusivity are cm2/s
C Units for solubility are cm3(STP)/[cm3 polymer-cmHg].

alcohols, and aromatic hydrocarbons. As shown in Table 3. 1, the
molar volumes of these substances vary from 32.4 to 147.4 cm3/ mole

and the solubility parameters vary from 5.3 to 29.7 (J / cm3)1/ 2 (2, 10,

28). The values for the membrane separation parameters, P1, Di’s, and
S1 measured for these substances are summarized in Table 3.2. These
data illustrate that permselectivity for these substances in the silicone
elastomer membrane is determined predominantly by the relative
solubilities. The solubilities vary by as much as four orders of
magnitude whereas the diffusivities for most of the substances vary by
less than a factor of ten. However, a comparison between the
diffusivities of the alcohols and those of the alkanes illustrates the
influence of the silica filler on the rate of mass transport. The
diffusivities for the alcohols are very low and exhibit no apparent
dependence upon molar volume. It is clear that retention by the
highly polar silica filler must be considered to enhance the predictive

value of the model.

Distribution selectivity
The constant a and the solubility parameter for the membrane

stationary phase, 85, from Equation 3.16 were calculated

simultaneously. Rearrangement of Equation 3.16 yields the following

relation:

(RT/v,)(1n(K,) + 1) = 2-(5S - al.81+ (a2 - 552) (3.37)

The plot of [RT/villln(Kl) + 1] vs. 61 in Figure 3.3 yields a straight line
with a slope of 2-[8S - on] = 21.8 and y-intercept of [on2 - 852] = -223.

55

600.0 --

500.0 --

400.0

300.0

200.0

100.0

(RT/v)ln[K+1]

0.0

 

 

-100.0

200.0 . i l l
5 1 0 1 5 20 25 30

Solubility Prameter

urb-
db

Key:

X = gases

dark circles = alkanes

circles = aromatics

dark diamonds = chloromethanes
diamonds = chloroethenes
triangles = bromomethanes

dark squares = alcohols.

Figure 3.3. Correlation between distribution ratio and solubility
parameter for substances in a silicone elastomer membrane at 25 °C.

By simultaneous solution of these equations, experimental values are
obtained for a = 4.8 (J/cm3)1/2 and 55 = 15.7 (J/cm3)1/2. The
solubility parameter reported in the literature for
poly(dimethylsiloxane) is 14.9 (J / cm3)1/ 2 (29). The value for the filled
silicone membrane is expected to be higher due to the polar nature of
the silica filler, whose estimated solubility parameter is 32.2

(J / cm3)1/ 2 (30). The solubility parameter for a mixture is estimated
from the contributions of the individual components according to
Equation 3.9 (8). When the solubility parameter values and the volume
fractions (<1)p = 0.75, (bf = 0.25) for the polymer and filler are
substituted into Equation 3.9, the calculated solubility parameter for
the stationary phase is 19.2 (J / cm3)1/ 2. The discrepancy between this
calculated value and the experimental value of 15.7 (J / cm3)1/ 2
suggests that the filled membrane does not exhibit the mass transport
properties that would be expected for a homogeneous mixture of the
individual phases. In addition, the filler is impermeable so that
sorption occurs only in the volume associated with the polymer/ filler
interfacial layer. Since the volume of this interfacial layer is difficult to
define, the experimentally determined value for 53 will be used in the

present model.

The experimental values for the distribution ratios and the
theoretical values calculated from Equation 3.16 are given in Table 3.3.
The distribution selectivities, K1/ K], with respect to methane and to
methanol were determined experimentally and were calculated using
the model described by Equation 3.17. These values are presented in
Table 3.4.

57

Table 3.3. Experimental and theoretical distribution ratios for

substances in a silicone elastomer membrane, at 25 °C.

compound

gases

nitrogen

oxygen

argon

carbon dioxide
alkanes

methane

ethane

propane

butane

pentane

hexane

heptane

aromatic hydrocarbons
benzene

toluene
ethylbenzene
chloromethanes
chloromethane
dichloromethane
chloroform
carbon tetrachloride
chloroethenes
chloroethene

1 , 1 -dichloroethene
trichloroethene
tetrachloroethene
bromomethanes
bromomethane
dibromomethane
bromoform
alcohols
methanol

ethanol

1 -propanol
l-butanol

distribution ratio

 

exp.

0.10
0.19
0.19

1.9

0.60
2.3
9.7

12
120
190
530

210
580
1900

13
93
180
320

13
100
370

1400

16
290
3900

950
2100
2100
2200

theor.

0.090
0.20
0.51
0.99

0.68
2.7
3.1
9.5

23
80
200

310
650
1600

39
79
180
200

1 2
120
330
880

37
550
2700

390
1200
4000

1 3000

Table 3.4. Experimental and theoretical distribution selectivities
for substances relative to methane and to methanol in a silicone
elastomer membrane at 25 °C.

distribution selectivity

 

relative to methane relative to methanol

compound e_xp_. theor. e_xp; theor.
gases

nitrogen 0.17 0.13 1.1X10'4 2.3X10'4
oxygen 0.31 0.30 2.0X10‘4 5.2X10'4
argon 0.31 0.75 2.0X10'4 1.3X10‘3
carbon dioxide 3.2 1.5 2.0X10'3 2.5X10'3
alkanes

methane 1.0 1.0 6.3X10‘4 1.8X10'3
ethane 3.8 4.0 2.4x10-3 7.0x10-3
propane 16 4.5 0.010 8.0X10‘3
butane 20 14 0.013 0.025
pentane 190 34 0.12 0.059
hexane 320 120 0.20 0.21
heptane 880 290 0.56 0.51
aromatic hydrocarbons

benzene 350 450 0.22 0.79
toluene 950 950 0.60 1.7
ethylbenzene 3 1 00 2400 2.0 4.2
chloromethanes

chloromethane 2 l 5 7 0.0 1 4 0.099
dichloromethane 1 50 l 20 0. 10 0.20
chloroform 310 270 0.1 9 0.47
carbon tetrachloride 530 290 0.33 0.50
chloroethenes

chloroethene 2 2 1 7 0.0 14 0.030

1 , 1 -dichloroethene 170 1 80 0. l 1 0.3 1
trichloroethene 6 1 0 480 0.38 0.83
tetrachloroethene 2400 1 300 1.5 2.3
bromomethanes

bromomethane 26 54 0.017 0.095
dibromomethane 480 800 0.30 1.4
bromoform 6500 3900 4.1 6.9
alcohols

methanol 1600 570 1.0 1.0
ethanol 3500 1800 2.2 3.1
l-propanol 3500 5900 2.2 10
l-butanol 3600 20000 2.3 34

59

The correlation between the experimental and theoretical values
appears quite reasonable for most of the substances. Whereas the
distribution ratios vary over a range greater than four orders of
magnitude, the difference between the experimental and theoretical
values is typically within a factor of two or three. With few exceptions,
the selectivity data show similarly good correlations. The most
significant discrepancy is seen for l-butanol, where the theoretical
distribution selectivity is a factor of six greater than the experimental
value. The experimental selectivities for the alcohols are quite similar,
as are the solubility parameters (Table 3.1). Conversely, the
theoretical selectivities for the alcohols more closely follow the molar
volume than they do the solubility parameter. The theoretical
selectivities are consistent with the experimental selectivities for the
other classes of substances studied. These data suggest that the -OH
group dominates the sorption process for the alcohols.

Diffusion selectivity
If no adsorption on the filler occurs, the diffusivity of a molecule
in a given membrane is dependent upon the size of the molecule and

is independent of chemical properties (Equation 3.20). With
correction for tortuosity (Equation 3.25), a plot of ln[(l + (bf/2)0(D1.S)]

vs. v11/3 is shown in Figure 3.4 for substances in the filled membrane.
Although all substances within a given class exhibit a linear
relationship, a single line is not observed for all classes as predicted

theoretically.

The presence of two distinct phases in the membrane, a non-
polar polymer phase and a polar silica phase, results in a marked
decrease in diffusive flow for the substances with greater hydrogen-
bonding character. As the functional groups exhibit greater hydrogen
bonding (i.e. «OH > -Br > --C1 > -CH3), the behavior deviates further
from a simple correlation with molar volume. These deviations are
predicted by Equation 3.27. In the most extreme case, the
diflusivities of the alcohols show no correlation with molar volume,
which suggests that only the partial molar volume of the -OH group is
involved in retention on the silica filler. For clarity, the aromatic
hydrocarbons and chloroethenes are not shown in this plot. The
diffusivity behavior of the aromatic hydrocarbons closely follows that of
the alkanes and the chloroethenes exhibit transport properties very

similar to the chloromethanes.

If the alkanes are assumed to diffuse through the membrane

without retention by the silica (k'i = 0), then the slope of the

regression line in Figure 3.4 gives the value for the polymer-
dependent term, 0, in Equation 3.27, while the pre-exponential term,
Do’p, is found from the intercept (not shown). This plot suggests that

diffusion in the polymer is described by:

Di.p = 8.25X10'4-expl-1.060v11/3] (3.38)

In the diffusion-retention (D-k) model of Equation 3.27 for
diffusivity in the filled elastomer, both the physical and chemical
properties of the system are considered. To predict diffusivities in

61

'10.0 T-

-11.0

 

“:1
f: -12.0
.2
m
3
1': -13.o --
D
C
-14.o --

M

-15.0 i i i 4. i
3.00 3.50 4.00 4.50 5.00 5.50

 

 

(Molar Volume) 1’3

Key:

X = gases

dark circles = alkanes

dark diamonds = chloromethanes
triangles = bromomethanes

dark squares = alcohols.

Figure 3.4. Correlation between difl’usivity, corrected for tortuosity,
and the molar volume for substances in a silicone elastomer
membrane at 25 °C.

62

the filled elastomer, it is necessary to estimate k'i by means of either

Equation 3.34 or 3.35. In the model described by Equation 3.34, the

proportionality constants A and B were determined from a plot of the
surface free energy, [RT/(N1/30v12/3)]0[ln(k'1) — 1n(Vf/Vp)] vs. the

cohesive energy density, 812, where the actual filler to polymer volume

ratio, Vf/Vp = 0.33, was used. From this plot, shown in Figure 3.5, it

was determined that A = 1.84 and B = -569 when the Avogadro's
number term, N1/ 3, is incorporated into these parameters. The

solution for the molar adsorption coefficient now becomes

1n(k'1) = -1.10 + (v12/3/(RT)1-[1.34-5,2 - 539) (3.39)

The model described by Equation 3.35 requires knowledge of

the partial molar volumes of the surface-active functional groups, v'i.

These partial molar volumes have been defined by Fedors (31) and are
given in Table 3.5.

Table 3.5. Partial molar volumes, v'i, for surface-active functional
groups from Reference 3 1 .

functional group molar volume, cm3[mole
Cl 24.0
Cl(disubstituted) 26.0
Cl(trisubstituted) 27.3
Br 30.0
Br(disubstituted) 3 1 .0
Br(trisubstituted) 32.4
OH 10.0

16.00 --
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00

Surface Free Energy

-2.00
-4.00
-6.00

 

 

r r I r r l
l I l I I l

0 100 200 300 400 500 600 700 800 900

unu-
an:
un-

Cohesive Energy Density

Key:

X = gases

dark circles = alkanes

circles = aromatics

dark diamonds = chloromethanes
diamonds = chloroethenes
triangles = bromomethanes

dark squares = alcohols.

Figure 3.5. Correlation between surface free energy,
[RT/ (N l/ 30v,” 3)]-[ln(k'1) - anf/Vpn, and cohesive energy density,
8‘2, for substances in a silicone elastomer membrane, at 25 °C. The

line is fitted to the halogenated compound and alcohol data only.

Partial molar volumes were not used for the gases, alkanes, and
aromatic compounds, since no significant orientation effects are

predicted for these substances. For these substances, it was assumed

that V, = v1. As noted previously, a value for the active volume ratio,
Vf/Vp, was not known. By comparing the experimental values for
ln(k'1) and the theoretical values for 1n(K'1) for the series of alcohols,

the active volume ratio was estimated. Values for 1n(k'1) were

determined from Equation 3.24 using experimental diffusivities and

Equation 3.36 where
ln(k'1) = ln[((8.25X10‘4/D1.S)-exp(-1.06-v1/3)} - 1] (3.40)

Theoretical values for ln(K',) were determined from Equation 3.35

where

1n(k'1) - lnnrf/vp) = 1n(K',) = [vi/(RUNS, - 14.9)2
- [v'1/(RT)]-[81-32.2]2 (3.41)

These results are summarized in Table 3.6.

Table 3.6. Data for determining the active volume ratio, Vf/Vp, in a
silicone elastomer membrane at 25 °C.

 

ln(k'i) ln(K'i) InN'f/Vp) =
compound Egn. 3.39 Egn. 3.41 Lfllliifld
methanol 3.92 3.57 0.35
ethanol 3.49 2.75 0.74
l-propanol 2.94 2.43 0.51
l-butanol 2.56 2.29 0.27

65

The mean value for the active volume ratio is 1.6, which is
approximately five times greater than the total volume ratio, Vf/Vp =
0.33. This result is consistent with the expectation that the active
filler surface area or interfacial volume is expected to be greater than

the actual volume of the filler.

For the silica-filled elastomer, the solution to the D-k model

using the surface areas of sorbed substances is given by

I)LS = 8.25X10‘40exp[-1.060vi1/3I/[1
+ 0.330exp{[v13?-/3/(R’I‘)]-[1.8405!2 - 569]} (3.42)

The solution using the partial molar volumes of the surface-active

functional groups is given by

DLS = 8.25X10'40exp[-1.06-v11/3l/[1
+ 1.6-exp{[v1/(RT)]°[61- 14.9]2
- [v'i/(RT)]0[51-32.2]2}] (3.43)

Both of these solutions were applied to the substances studied. The
results are given in Table 3.7 along with experimental diffusivities and
theoretical values calculated from Equation 3.38 for non-retained
transport. The D-k models (Equation 3.42 and Equation 3.43)
generally exhibit a better correlation with the experimental values
than does the non-retained transport model. Both D-k models
successfully predict little retention on the filler by the alkanes but
widely varying degrees of retention for the other organic compounds.

66

Table 3.7. Experimental and theoretical difl’usivities for substances
in a silicone elastomer membrane at 25 °C.

W e_xp.
gases

nitrogen 2 1
oxygen 2 1
argon 21
carbon dioxide 13
alkanes

methane 16
ethane 1 1
propane 6.4
butane 6.3
pentane 4.5
hexane 3.5
heptane 3.2
aromatic hydrocarbons
benzene 4.9
toluene 3.5
ethylbenzene 1.7
chloromethanes
chloromethane 1 l
dichloromethane 7.9
chloroform 4.9
carbon tetrachloride 2.9
chloroethenes
chloroethene 9. 1
1.1-dichloroethene 5.8
trichloroethene 3.7
tetrachloroethene 2.4
bromomethanes
bromomethane 9. 1
dibromomethane 4.2
bromoform 1.3
alcohols

methanol 0.42
ethanol 0.40
l-propanol 0.47
l-butanol 0.50

diffusivity, x10-6 cm2/s

theor.

 

—Eqn. 3.38

No Retention

28
28
14
15

16

10

7.8
5.9
4.7
3.8
3. l

7.2
5.4
4.2

15
12
8.5
6.3

1 l

8.8
7. l
5.9

14
l l
7.5

22
13
9.4
7.0

67

ER. 3.42 Eqn. 3.43

D-k Model

27
26
13
14

15

9.8
7.5
5.6
4.4
3.5
2.9

4.4
3.6
2.9

8.0
6.3
5.0
4.7

9.3
5.6
4.3
3.3

8. 1
2.4
1.6

0.41
0.64
0.64
0.57

D-k Model

28
27
14
15

16

10

7.8
5.9
4.7
3.8
3. l

7.2
5.4
4.2

9.0
7.5
6.0
5.3

9.6
6.4
5.0
3.9

10
3.4
2.4

0.37
0.52
0.49
0.42

Table 3.8. Experimental and theoretical (D-k model, Equation 3.42)
difiusivity selectivities for substances relative to methane and to
methanol in a silicone elastomer membrane at 25 °C.

diffusion selectivity

 

relative to methane relative to methanol

compound e_xg theor. exp. theor.
gases

nitrogen 1.3 1.8 50 66
oxygen 1.3 1.8 50 63
argon 1.3 0.90 50 3 2
carbon dioxide 0.8 1 0.92 3 1 3 3
alkanes

methane 1.0 1.0 3 8 36
ethane 0.69 0.65 26 23
propane 0.40 0.50 1 5 l 8
butane 0.39 0.38 1 5 1 3
pentane 0.28 0.30 1 1 1 1
hexane 0.22 0.24 8.4 8.5
heptane 0.20 0.19 7.6 6.9
aromatic hydrocarbons

benzene 0.31 0.24 1 2 8.6
toluene 0.22 0.22 8.4 7.7
ethylbenzene 0.1 1 0.18 4.1 6.5
chloromethanes

chloromethane 0.69 0.38 2 6 1 3
dichloromethane 0.49 0.30 1 9 1 1
chloroform 0.3 1 0.26 1 2 9.5
carbon tetrachloride 0. 1 8 0.29 6.9 1 0
chloroethenes

chloroethene 0. 57 0.58 2 2 2 1
1, l -dichloroethene 0. 36 0.3 1 1 4 1 1
trichloroethene 0.23 0.24 8.8 8.4
tetrachloroethene 0. l 5 0. 1 8 5.7 6.6
bromomethanes

bromomethane 0. 57 0.39 2 2 1 4
dibromomethane 0. 26 0. 1 0 1 0 3.6
bromoform 0.081 0.071 3.1 2.5
alcohols

methanol 0.026 O. 028 1.0 1.0
ethanol 0.025 0.032 0.95 1.1
1 -propanol 0.029 0.030 1.1 1 . 1
1-butanol 0.031 0.027 1 2 0.97

The solution to the D-k model given in Equation 3.42 was used
to determine the diffusion selectivities (Equation 3.36) relative to
methane and to methanol. The experimental and D-k model diffusion
selectivities are given in Table 3.8. The results from the D-k model
show reasonable correlation to experimental selectivities relative to a
non—retained reference (methane) as well as a highly retained

reference (methanol).

Enrichment

The correlations between the experimentally determined
enrichment factors, 81/], and the product of the theoretical diffusion

and distribution selectivities, (D1/ Dj)0(Ki/ K1), are given relative to

methane and relative to methanol in Table 3.9. The theoretical
distribution selectivities were determined based on Equation 3. 17 and
the diffusion selectivities were based on the D-k model given by the
combination of Equations 3.36 and 3.42. With the notable exceptions
of l-propanol and l-butanol, reasonable correlation is observed

between the experimental and theoretical enrichment factors.

For most of the substances studied, the deviation between the
experimental and theoretical values for the distribution selectivities
are opposite in direction from the diffusion selectivities.
Consequently, these errors compensate for one another, such that the
enrichment factors are accurately predicted. For some substances,
however, these deviations are in the same direction so that poorer
correlation between the experimental and theoretical enrichment

factors is observed.

69

Table 3.9. Enrichment factors for compounds relative to methane

and to methanol in a silicone elastomer membrane at 25 °C.

Theoretical values were obtained from the product of distribution
(Equation 3. 16) and diffusion selectivities (D-k model, Equations

3.36 and 3.42).

compound

nitrogen
oxygen

argon

carbon dioxide
alkanes

methane

ethane

propane

butane

pentane

hexane

heptane

aromatic hydrocarbons
benzene

toluene
ethylbenzene
chloromethanes
chloromethane
dichloromethane
chloroform
carbon tetrachloride
chloroethenes
chloroethene

l , 1 -dichloroethene
trichloroethene
tetrachloroethene
bromomethanes
bromomethane
dibromomethane
bromoform
alcohols

methanol

ethanol

1 —propanol
1-butanol

enrichment factors

 

relative to methane

100
110

70

mm;

250
740

relative to methanol

exp.

5.2X10'3

0.010
0.010
0.063

O 01

”93.0 9°92“? PPE‘P 5‘9”?” Eff-20.0
o:

umwo “ow memw wwmm mom wuwww

PPP!‘

than;

0.015
0.033
0.042
0.085

0.063

O
H
hwhfl

°°"‘°° $959.09.

C)

.. .. “@PP 999? .
“mmo mwm mama wwww om» mmmww

wool-I

.hv—uhr—a

Error analysis (see Appendix) indicates that the estimated
relative standard deviations for the diffusivity and distribution
selectivity measurements are 60 % and the relative standard deviation
for the enrichment factor measurements are 14 %. In addition,
experimental error may result from absorption of a substance into the
walls of the sampling bag used to prepare the mobile phase gas
mixtures.

Graphically, the correlation for experimental and theoretical
values for the distribution, diffusion, and permeation selectivities
relative to methane are shown in Figure 3.6. The same correlation for
selectivities relative to methanol are shown in Figure 3.7. These plots

demonstrate the predictive capabilities of the model.

Although the predictive ability of the model was quite good, it
could be improved by an expanded solubility parameter treatment that
takes into account specific chemical interactions between the sorbed
substances, the polymer, and the filler. The consistency of the model
possibly suffers from the use of molar volumes and solubility
parameters that were not all generated by a single researcher.
However, the reasonable application of a predictive permeation model
using readily available parameters has been demonstrated for a wide

variety of substances.

71

10.00

8.00

6.00

4.00

2.00

Experiment

0.00

-2.00

 

-4.00

 

 

-4.00 -2.00 0.00 2.00 4.00 6.00 8.00 10.00

38%

circles = permeation
diamonds = distribution ratio
squares = diffusivity.

Figure 3.6. Correlation between experimental and theoretical
selectivities for substances relative to methane in a silicone
elastomer at 25 °C.

72

6.00

4.00

2.00

0.00

-2.00

Experlment

-4.00

-6.00

-8.00

 

 

-1000 r r r r 4 IL

I I I I I

-10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00

Theory

KBF

circles = permeation
diamonds = distribution ratio
squares = diffusivity.

Figure 3.7. Correlation between experimental and theoretical
selectivities for substances relative to methanol in a silicone
elastomer at 25 °C.

73

REFERENCES

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

C. Hansen and A. Beerbower, Solubility parameters, in: A.

Standen (Ed.), Kirk-Othmer Encyclopedia of Chemical
Technology, Suppl. Vol. 2nd. Ed.: 1971.

A. F. M. Barton, Solubility parameters, Chem. Rev. 1975, 75, 731.

H. Burrell, Solution Properties: Solubility Parameter Values, in: J.
Brandrup and E. H. Immergut (Eds.), Polmer Handbook, 2nd
ed.; Wiley-Interscience: New York, NY; 1975.

B. Schneier, J. Appl. Polym. Sci. 1972, 16, 2343.

A. F. M. Barton, Handbook of Polymer-Liquid Interaction
Parameters; CRC Press: Boca Raton, FL; 1990.

H. W. Starkweather, Jr., Macromolecules 1977, 10, 1161.

J. H. Hildebrand and R. L. Scott, The Solubility of
Nonelectrolfies, 3rd ed.; Reinhold: New York, NY; 1950.

J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott, Regular and
Related Solutions; Van Nostrand-Reinhold: Princeton, NJ; 1970.

B. L. Karger, L. R. Snyder, and C. Eon, Anal. Chem 1978, 50,
2126.

V. Stannett, Simple gases, in: J. Crank and G. S. Park (Eds.),
Diffusion in Polmers; Academic Press: New York, NY; 1968.

H. F. Mark, N. M. Bikales, C. G. Overberger, G. Menges, and J. I.

Kroschwitz (Eds.), Encyclopedia of Polmer Science and
Engineering, Vol. 3; Wiley-Interscience: New York, NY; 1985.

(12) J. M. Prausnitz and F. H. Shair, A.I.Ch.E. J. 1961, 7, 682.

74

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

J. C. Giddings, M. N. Myers, L. McLaren, and R. A. Keller,
Science 1968, 162, 67.

W. W. Brandt, J. Phys. Chem, Wash. 1959, 63, 1080.

K. D. Ziegel, H. K. Frensdorff, and D. E. Blair, J. Polym Sci. 1969,
A-2, 809.

R. M. Barrer, J. A. Barrie, and N. K. Raman, Polymer 1962, 3,
605.

R. M. Barrer, J. A. Barrie, and M. G. Rogers, J. Polym Sci. 1963,
A-l. 2565.

A. S. Michaels and H. J. Bixler, J. Polym Sci. 1961, 50, 413.

G. J. van Amerongen, Rubber Chemistry and Technology 1964,
37 . 1065.

S. Wu, J. Phys. Chem 1968, 72, 3332.

A. Beerbower, Surface free energiz A new relationship to bulk
energies, J. Colloid Interface Sci. 1971, 35, 126.

L. B. Westover, J. C. Tou, and J. H. Mark, Anal. Chem 1974, 46,
568.

Standard test method for C1 through C5 hydrocarbons in the
atmosphere by gas chromatography, in: 1990 Annual Book of
ASIIM Standards: Volume 1 1.03, ASTM, 1916 Race Street,
Philadelphia, PA, 19103-1187.

J. C. Fjeldsted, presented at the Instrument Society of America
International Conference and Exhibition, New Orleans, LA, 1990.

75

(25)

(26)

(27)

(28)

(29)

(30)

(31)

Analytical Sciences Mass Spectral Data Base, The Dow Chemical
Co., Midland, MI, internal communication, based on method by
V. Caldecourt, Anal. Chem 1955, 27, 1670.

M. A. LaPack, J. C. Tou, and C. G. Enke, Anal. Chem 1990, 62,
1265.

M. E. Hodgson, Filtr. and Separ. 1973, July, 418.

A. F. M. Barton, Handbook of Solubiligg Parameters and cher
Cohesion Parameters; CRC Press: Boca Raton, FL; 1983.

G. L. Lee, S. A. Stern, J. E. Mark, and E. Hoffman, Investigation of

Structure-Sermeability Selationships of Silicone Solyrper
Sembranes: Final Report October 1982 - September 1986, Gas

Research Institute, Chicago, IL.

P. J. Shoenmakers, H. A. H. Billiet, and L. de Galan,
Chromatographia 1982, 15, 205.

R. F. Fedors, Polym Eng. Sci. 1974, 14, 147.

76

CHAPTER 4

A Model for Characterizing and Predicting
Membrane Extractions based on
Chromatographic Retention

 

As demonstrated in Chapter 3, the capacity to separate
components in a mixture can be predicted utilizing fundamental
separation principles. Chromatography is governed by these same
fundamental principles and can therefore be a useful tool for
characterizing the sorption and transport properties of polymeric
materials (1, 2). A membrane extraction model based upon
chromatographic principles is developed in this chapter. The effect of
chemical properties and experimental conditions on permeability
parameters are discussed in the context of this model. Finally, the
model provides a quantitatively useful rule of thumb with simple
correlations between membrane extraction efficiencies and such

readily available data as boiling points and solubility parameters.

EXPERIMENTAL METHODS

Gas chromatography
The chromatography column was a 15 meter-long, 250 (rm-i.d.,
1 (rm-film thickness DB-l (poly(dimethylsiloxane) bonded phase)

capillary from J&W Scientific, Folsom, CA. The helium or nitrogen

77

mobile phase linear velocity was 50 cm/s. The column temperature
was 25 °C isothermal. Mass analysis of the chromatographic effluent
was performed with the first quadrupole of a Finnigan TSQ-70 GC/ MS.
The scan rate was 0.2 seconds/ scan for a 10-300 dalton range. The
secondary electron multiplier voltage was -1000 V. The dynode
voltage was ~2000 V.

Membrane extraction

A flow-through silicone hollow fiber membrane separator with
mass spectrometric detection was used for the measurement of the
permeation data. The membrane was a 2.5 cm length of Dow Corning
SilasticTM Medical Grade Tubing (0.0635 cm o.d., 0.0305-cm i.d., 69 %
poly(dimethylsiloxane), 3 1 % silica by weight) mounted in a stainless
steel tee (3). The nitrogen mobile phase flow through the hollow fiber
membrane was 100 cm3 / minute. The membrane temperature was 25
°C isothermal. The permeation measurements were made with the
ME device interfaced directly with a Hewlett-Packard 5971-A MSD
quadrupole mass spectrometer modified for process analysis
applications (4). The scan rate was 0.3 s/ scan for a 10-180 dalton

range. The electron multiplier voltage was -1500 V.

Reviewing the solution-diffusion model (5), permeation through
a membrane may be described by three processes: 1) selective
partitioning of a substance between the membrane stationary phase
and the mobile phase, 2) selective diffusion of the substance through

the membrane phase, and 3) desorption of the substance from the

78

membrane phase into a sweep fluid or vacuum. The permeation rate,

F1, for a component, i, is described by Fick's first law:

Fl = A'DI’S.K1.C1'm/d (4.1)

where A is the membrane surface area, D51 is the diffusivity of
component i in the stationary (membrane) phase, K1 is the distribution

ratio for component i in equilibrium between the membrane stationary

phase and the mobile phase, 01,111 is the concentration of component i

in the mobile phase, and d is the membrane thickness. The product
Di,sKi is the permeability constant, P1, for component i in the
membrane. Just as with chromatography, the ability of a membrane
phase to separate two components from a mobile phase is dependent
upon both thermodynamic (distribution ratio) and kinetic (diffusivity)
parameters. The analytical power of membranes lies in their ability to
provide an enriched analyte stream to the analyzer. The permeation
enrichment factor, 81/1, for component i over component 1 is given by
the relative permeation rates of the two components normalized with

respect to their concentrations in the sample

81/] = [Fr/Fjl/[C1,m/Cj,m] = [D1,s/Dj,s]‘[K1/Kj] = Pi/Pj (4.2)

The method for determining membrane permeation parameters
such as distribution ratios and diffusivities is described in detail in the
Appendix of this work. In this chapter, the two selective processes
(distribution and diffusion) are discussed separately and then their

implications to the extraction process are presented.

79

RETENTION AND DISTRIBUTION

The difference in the ability of two different phases to solvate a
substance is a major driving force for many membrane and
chromatographic separation processes. These solvation processes
have been shown to exhibit a fundamental relationship that may be
described by regular solution theory, as modified by Flory-Huggins (6-
8). Hildebrand et. al. (9) have proposed that the solubility of a gas in a
liquid solvent can be described as a two-step process involving first
the compression of the gas into some hypothetical liquid state
followed by sorption of this hypothetical liquid into the solvent. The
extension of this model to gases dissolving in a polymer, with Flory-
Huggins correction, has been given in Chapter 3 as follows:

mm = [vi/RT1°[(51- 002 - (a. - 5.321 - 1 (4.3)

Where K1 is the concentration distribution ratio tots/Chm), v1 is the

molar volume of the partitioning substance 1, R is the ideal gas
constant, T is the absolute temperature, 81 and 65 are the solubility
parameters for the partitioning compound 1 and the stationary phase,
respectively, and a is an experimentally determined constant that
corrects for non-ideal behavior and approximates the solubility
parameter of the hypothetical compressed mobile phase. Values for
molar volumes, solubility parameters (7, 8, 10), and boiling point

temperatures (1 1) used in these studies are presented in Table 4.1.

Table 4. 1. Molar volumes, Hildebrand solubility parameters (7 , 8,
10), and boiling points (11) for the compounds used in this study.

compound
nitrogen

oxygen

argon

carbon dioxide
methane

ethene

ethane

propane

butane

pentane

hexane

heptane

benzene

toluene
ethylbenzene
chlorobenzene
chloromethane
dichloromethane
chloroform
carbon tetrachloride
chloroethene

1 , 1 —dichloroethene
trichloroethene
tetrachloroethene
bromomethane
dibromomethane
bromoform
water

methanol
ethanol

1 -propanol
2-propanol

1 -butanol
acetone
2~butanone

yi, cm3[mole

32.4
33.0
57. 1
55.0
52.0
65.0
70.0
89.4
101.4
1 16.2
131.6
147.4
89.4
106.8
123. 1
102. 1
55.4
63.9
80.7
97. 1
68. 1
79.0
90.2
101. l
56. 1
68.9
87.5
18.0
40.7
58.5
75.2
76.8
91.5
74.0
90. 1

81

éll (MP3! 1/2

5.3

8.2
10.9
12.3
1 1.6
13.5
13.5
13.4
13.9
14.3
14.9
15.1
18.8
18.2
18.0
19.4
19.8
19.8
19.0
17.6
16.0
18.6
18.8
19.0
19.6
22.3
21.8
47.9
29.7
26.0
24.3
23.3
23.3
20.3
19.0

T._K

77.4

90.2

87.5
194.7
109.2
169.5
184.6
231. 1
272.7
309.3
342.2
371.6
353.3
383.8
409.4
405.2
249.0
313.3
334.9
349.7
259.8
310.2
360.2
394.2
276.8
370.2
422.7
373.2
338. 1
351.7
370.6
355.6
390.4
329.4
352.8

For identical mobile and stationary phases, the
chromatographically determined distribution ratio for an analyte will
be the same as that determined from permeation measurements. The
equilibrium distribution of a substance between the stationary and
mobile phases may be determined from chromatographic retention

times and the phase ratio using the following relation:

Ki = kl'B = [(tri'to)/to].[vm/Vs] (4-4)

where k1 is the molar partition coefficient, tn is the elution time for a

retained component i, to is the elution time for a non-retained

component, and [3 is the volumetric phase ratio.

The distribution ratios for several substances obtained from CC
and ME measurements are given in Table 4.2. The distribution ratio
for the permanent gases is so low that their retention in the
chromatographic stationary phase is essentially zero. The time
observed for the elution of the air peak (N2, 02, Ar, and C02 are not
separated) is taken to be to. In practice, nitrogen carrier gas is more
representative of the air sample matrix that is reported in most ME
applications, while helium is a more common carrier gas since its
lower density allows for higher linear velocities (12). As demonstrated
in Table 4.2, no significant differences are observed in the GC

retention time data when the two different carrier gases are used.

The ME data described below were obtained with nitrogen

carrier gas while the GC data were obtained with helium carrier gas.

82

Table 4.2. Experimental distribution ratios, K1, determined by ME

andGCat25°C.

compound
nitrogen

oxygen

argon

carbon dioxide

methane

ethene

ethane

propane

butane

pentane

hexane

heptane

benzene

toluene

ethylbenzene

chlorobenzene

chloromethane

dichloromethane

chloroform

carbon tetrachloride

chloroethene

1 , 1 -dichloroethene

trichloroethene

tetrachloroethene

bromomethane

dibromomethane

bromoform

water

methanol

ethanol

_ 1-propanol
2-propanol

l-butanol

acetone

2-butanone

ME with N2
mobile phase

(110
(119
(119
L9
(160
112
2&3
9J’
12
120
190
530
210
580
1900
1600
13
93
180
320
13
100
370
1400
16
290
3900
340
950
2100
2100
834
2200
1000
1500

GC with He
mobile phase

\lHNv-‘HOOOOO

$Eme99999999
CO

310
870
2200
1800
12
81
190
330
19
76
450
1300
28
410
2200
9.3
15
37

1 10
56
310
49
140

G0 with N2
mobile phase

9999

180
490
290
820
2000
1700

77
180
300

73
420
1200

380
2100

23
41
120
59
330
50
150

Within experimental error, most of the compounds that exhibit weak
or no hydrogen bonding show good agreement for the two techniques.
The effect of the silica particles dispersed in the membrane is
apparent when comparing the distribution ratios obtained by the two
techniques for the strong hydrogen bonding substances. The silica
provides a hydrogen-bonding component to the membrane, resulting
in a much higher affinity for compounds that exhibit hydrogen bonding

than does the otherwise non polar silicone phase.

Just as with chromatographic systems, the capacity of the
membrane to perform thermodynamic separations decreases as the
temperature of the system increases. This effect is shown in Figure
4.1 in the plot of K1 vs. T for various components. Due to the presence
of the silica in the membrane, a dramatic difference in the position of
the curves for l-butanol is seen when comparing the ME data (Figure
4.1a) with the GC data (Figure 4.1b). Since they exhibit little affinity
for the silica, the non polar compounds in these plots demonstrate
nearly identical behavior between the two systems. The temperature
dependence of the distribution ratio illustrated in these plots is given
by the following relation:

a(1n(K,])/a(1/T) = -AHSi/R (4.5)

where AHSi is the difference in enthalpy of solution for the substance
in the stationary phase and the mobile phase (AHSi = Hs,(stationary
phase) - HSi(mobile phase)). Values for AHSi were obtained from the

slope of a plot of 1n[K1] vs. l/T for selected compounds and are

84

Distribution Ratio

Distribution Ratio

2500 -r

2000 ..

1500 ..

1000 --

500 .-

 

(a)

 

 

2500 --

1500 ..
1000 J-

$00--

 

Key:

X = carbon tetrachloride
square = l-butanol
diamond = chlorobenzene
triangle = toluene.

20 40 60 80 1 00

Temperature, °C

(b)

l
f

'\
20 40 60 80 100

Temperature, °C

Figure 4. 1. The efiect of temperature on the stationary
phase] mobile phase distribution ratio, 8,, obtained by ME (a) and by

85

presented in Table 4.3. Generally, AHS, values for gas-phase organic

compounds are negative, and the magnitude of AHsi indicates the

ability of the silicone stationary phase to extract the compound from

the mobile phase. Deviations in these AHsi determinations may result

from interactions between the compounds and the silica filler as well
as imprecision in chromatographic elution time and permeation

measurements.

Table 4.3. Values for the heats of solution for selected compounds
in the membrane and chromatographic stationary phases.

H51 (kJ / mole)

 

compound M Q
nitrogen —8

heptane -27 -33
toluene -34 -34
chlorobenzene -48 -36
carbon tetrachloride -3 1 -29
1 -butanol -46 - 3 1

By the Hildebrand rule (6), a strong correlation exists between
the solubility parameter and the boiling point, Tbl, for a substance.

Thus, a correlation also exists between lanI] and Tbi where, for a

homologous series of compounds, the correlation may be given by (13)

lanll = m.Tbi + b (4.6)

86

(a)

 

 

c 9.00 --
I

s a o
:3 7.00 "' 00°
3 5.00 ..
2 o
"' “=- 3.00 --
'5 g l
8’ 1.00 «-
_.I
To I
5 4.00 -L
‘25

-3.00 i i i i

50 150 250 350 450
Boiling Point Temperature, °C
(b)

9.00 ..
C
.9
‘5 7.00
:9
‘6
5 5.00
2 0
~ 3: 3.00
'6 BE
8 1.00
.1
Ta
5 -1.00
E

-3.00

 

 

 

Boiling Point Temperature, °C

W
square = weak or non-hydrogen bonding compound
circle = strong hydrogen bonding compound.

Figure 4.2. The correlation of the distribution ratio, K4, with boiling
point, Tm, at 25 °C. obtained by ME (a) and by GC (b).

87

where M is the slope and B is the y-axis intercept for the plot of 1n[K1]
vs. Tbi- A plot of land vs. Tbi is given for the ME and GC data in

Figure 4.2. The compounds that exhibit strong hydrogen bonding are
seen to deviate significantly from the straight line plot resulting from
linear regression of data for the compounds that exhibit weak or no
hydrogen bonding. For the silicone membrane at 25 °C. this linear
regression yields values for the slope, where m = 2.85X10'2, and for
the y-intercept, where b = -4.38. For the lowest boiling point
compounds, distribution ratios could not be determined by gas
chromatography because no retention was observed. However, even
with fewer data points, the chromatographic experiments yielded a
nearly identical line with a slope m = 2.87X10'2 and the intercept b =
-4.37. Most of the strong hydrogen bonding compounds exhibit ln[K1]
values that are higher than predicted by the straight line plot for the
ME experiments (Figure 4.2a). This result is consistent with the
affinity of these compounds for the silica in the membrane. In the
case of the GC data, a plot of le11 vs. Tm yields a negative deviation
from a straight line plot for the hydrogen bonding compounds (Figure
4.2b) because hydrogen bonding interactions result in boiling point
temperatures that are higher than predicted from dispersion

interactions alone (14).

The selectivity of the membrane to perform a given
thermodynamic separation on the basis of known boiling points can be
predicted from with a general form of Equation 4.6.

Ki/KJ = exp(2.85x1o-2-(Tb,-Tbj)) (4.7)

Table 4.4. Distribution selectivities for compounds over nitrogen
and heptane at 25 °C. Tb = predicted from boiling points (Equation

4.7):
4.3):
GC data.

99mm
nitrogen

oxygen

argon

carbon dioxide
methane

ethene

ethane

propane

butane

pentane

hexane

heptane

benzene

toluene
ethylbenzene
chlorobenzene
chloromethane
dichloromethane
chloroform
carbon
tetrachloride
chloroethene

1 , 1 -dichloroethene
trichloroethene
tetrachloroethene
bromomethane
dibromomethane
bromoform
water

methanol
ethanol

1 -propanol
2-propanol

1 -butanol
acetone
2-butanone

 

relative to nitrogen

relative to heptane

SP = predicted from solubility parameter theory (Equation
ME - experimental from ME data; GC = experimental from

 

113 3.13
1.0 1 .0

1.4 2.3

1.3 5.7

28 l 1
2.5 7.6

14 26

21 30

80 49
260 106
740 260
1900 890
4400 2200
2600 3400
6200 7200
13000 18000
1 1000 15000
130 430
830 880
1500 2000
2300 2200
180 130
760 1300
3200 3600
8300 9800
160 400
4200 6100
19000 30000
4600 1600
1700 4300
2500 14000
4300 44000
2800 28000
7500 150000
1300 2800
2600 4200

Mlb

1 .0
1.9
1.9
19
6.0
22

3700

21000
21000

22000
10000
15000

89

 

2.2x104
3.3x104
3.0x10-4
6.5x10-3
5.7x104
3.2x10-3
4.8X10'3
1.3x10-2
3.0x10-2
0.17

33
4.5x10-4
1.0x10-3
2.6X10‘3
5.0x10-3
3.4x10-3
1.2x10-2
1.4x10-2
2.2x10-2
4.3x10-2

M.;:
1.9x104
3.6X10‘4
3.6X10'4
3.6x10-3
1.1x10-3
4.1x10-3
4.3x10-3
1.3x10-2
2.2x10-2
0.22
0.33

1.0

0.40

1.1

3.5

3.1
2.4x10-2
0.17
0.35

0.60
2.4x10-2
0.20
0.69

2.7
3.0x10-2
0.55

7.4

0.64

1.8

3.9

4.0

1.6

4. 1

2.0

2.3

2.9x10-2
6.9x10-2
0.20
0.10
0.58
9.2x10-2
0.27

Examples of distribution selectivities are given in Table 4.4 along
with those predicted by modified regular solution theory (Equation
4.3) and by boiling point correlations (Equation 4.7). Since nitrogen is
assumed to be non retained by the GC stationary phase, the
selectivities compared with nitrogen cannot be presented for the
chromatographic data. Instead, distribution selectivities with respect
to heptane are presented for both ME and GC as well as the
selectivities predicted from Equation 4.7. Although the hydrogen
bonding substances deviate from the values predicted by Equation 4.7,
significant selectivities for these compounds (1) with respect to

nitrogen (j) are still predicted for the membrane.

The predictive models and the data demonstrate that the
distribution ratio selectivities increase as the molar volume (or
molecular weight) of the compounds increase within a series. For a
selectivity model, a factor of two or three difference between the
predicted values and the experimental values may be considered quite
good considering that one of the most widely used ME applications of
separating organic analytes from air is a process that favors the
analytes by one to four orders of magnitude. With a few exceptions,
most of the selectivity data relative to nitrogen meet this criterion. As
expected, the predictions based upon the boiling points show the
greatest deviation from the experimental data for the compounds that
exhibit strong hydrogen bonding. Using the solubility parameter
model, the predicted selectivity for 1-butanol is a factor of seven
higher than observed by the ME method. An expanded model (7, 15)
that contains specific solubility parameters for dipole interactions and

90

hydrogen bonding may provide better correlations. However, even the
simple models in the present work provide a reasonably quantitative

approximation.

Except for the strong hydrogen bonding compounds, the
selectivity values relative to heptane obtained by ME are in excellent
agreement with the values obtained by GC. The values predicted by
the solubility parameter model show less agreement for the most part
because heptane exhibits a factor of more than two higher distribution
ratio than is predicted by the model, as discussed in Chapter 3. In any
case, the thermodynamic relationship between the ME and the GC
processes is evident and the rules that guide the use of one technique

readily apply to the other.

BAND SPREADING AND DIFFUSION

The band widths of chromatographic peaks are highly diffusion-
dependent as described by the Van Deemter equation (16) for packed
columns and the Golay equation (17) for open tubes. The Golay

equation states that for open tubular columns, effective theoretical

plate height, h,, for a component is the sum of plate height
contributions from the stationary phase, his, and from the mobile

phase, him, where

hi = 111.8 '1' hi,m (4.8)

The plate height contributions in both phases are due to transport in
both the radial, r, and longitudinal, 1, directions in the column, where

91

111,5 = l'li,sr + hi,sl (4-9)

and

hi,m = hi,mr 1' hi,m1 (4.10)

Therefore, band spreading is due to longitudinal diffusion and radial

diffusion in both phases. Bandspreading in the stationary phase is
dependent upon the diffusivity, DLS of component i, in the stationary

phase of thickness d, the partition coefficient, k1, and the linear

velocity of the mobile phase, u, where

his, = [2/3]-[ki/(1+k1)2][d2/Di,s]u (4. 1 1)
and
111,81 = 20Di,S-k1/u (4. 12)

Bandspreading in the mobile phase is dependent upon the inner

radius, r, of the open tubular column, the partition coefficient, the

linear velocity of the mobile phase, and the diffusivity, Dim, of

component i in the mobile phase gas, where

hi,mr = [(1+60k1+1 1Oklzl/(24°(1+ki)2)][r2/Di.m]u (4. 13)

and

92

hi.ml = 2°DLm/u (4.14)

Values for Dim are readily estimated from the method developed

by Fuller, Shettler, and Giddings (18) where, in a helium mobile
phase,

Dl.m = 1.75X10'30T0[(M1+MHC)/(M1.MHC)]1/2
/{P'[(2V)1”3 + VHe1/312} (4.15)

where T is the absolute temperature, M1 and MHe are the molecular

weights for the component i and helium, respectively, and p is the gas

pressure. In the present model, the empirical molecular diffusion

volume for substance 1, (th, given by the sum of the empirical

diffusion volumes for the atoms comprising substance i and the atomic

diffusion volume of helium, VH6, are replaced by molar volume terms,

vi, given in Table 4.1, factored by Avogadro's number, NA, where
(2V)1 = Vi/NA (4. 16)
By combining and rearranging Equations 4.8, 9, 1 1, and 12, the

following quadratic equation is obtained for determining diffusivities in

the stationary phase:

0 = [2.k1/UI.D1.32 ' [hi-hl,m].Dl,S + [2/3]°[k1/(1+k1)2]°d20u (4. 17)

The solution for DLS is given by

93

131,3 = [hr‘h1,ml‘u/[4'krl
- {Ilhi-h1,m]°u/[4‘k)l)2 - [1/3l'ld'u/(1+k1)12}1/2 (4.18)

Experimentally, the plate height, h, is determined from the
column length, L, the experimental retention time, tn, and the band
Width at half maximum, W1, (19) where

bl = L'WiZ/(5.54.tri2) (4.1 9)

Calculated gas-phase diffusivities, longitudinal and radial
components of band spreading, and experimental plate heights are
summarized in Table 4.5 for the components of interest. The

measurements of W, are made with much less certainty for poorly

retained compounds. In fact, W, was impossible to determine for some

of these compounds under the present experimental conditions,
because only two or three data points could be obtained for an eluting
band, which was an insufficient number to obtain a measurable peak
profile. This common problem is difficult to resolve with a scanning
instrument (20). A thicker chromatographic stationary phase might
help alleviate this problem, but would result in extremely long
retention times and broad bands for the compounds with higher
boiling points. Recording the analog signal from, for example, a flame
ionization detector might provide more accurate profiles. However,
band overlap at higher temperatures would pose an even more serious
problem. The mass spectrometer provides an additional degree of

separation in such cases.

Table 4.5. Mobile phase difl’usivities, Dun, and chromatographic
band spreading components used to calculate difiusivities in the

stationary phase at 25 °C.
Di,m

compound (an. 4. 15)
nitrogen 0. 32
oxygen 0. 3 1
argon 0. 25
carbon dioxide 0. 26
methane 0. 28
ethene 0. 24
ethane 0. 24
propane 0. 2 1
butane 0. 20
pentane 0. 1 9
hexane 0. l 8
heptane 0. l 7
benzene 0. 2 1
toluene 0. 19
ethylbenzene 0. 1 8
chlorobenzene 0. 1 9
chloromethane 0. 25
dichloromethane 0. 24
chloroform 0. 2 1
carbon tetrachloride 0. 20
chloroethene 0. 23
1 , l -dichloroethene 0.22
trichloroethene 0. 20
tetrachloroethene 0. l 9
bromomethane 0. 25
dibromomethane 0. 23
bromoform 0. 20
water 0.40
methanol 0. 29
ethanol 0. 25
1 -propanol 0. 22
2-propanol 0.22
1 -butan01 0. 20
acetone 0. 22
2—butanone 0. 2 1

hi,mr

(Egn. 4.13)

95

1.2x10-3
1.2x10-3
1.5x10-3
1.4x10-3
1.3x10-3
2.4x10-3
2.4x10-3
3.2x10-3
7.4x10-3
9.3x10-3
1.6x10-2
2.1x10-2
1.5x10-2
1.9X10-2
2.2x10-2
2.0x10-2
3.5x10-3
8.1x10-3
1.3x10-2
1.6X10-2
4.6x10-3
8.6X10-3
1.7x10-2
2.0x10-2
5.5x10-3
1.5X10-2
1.9x10-2
1.9x10-3
3.4x10-3
6.5x10-3
1.3x10-2
9.2x10-3
2.0x10-2
8.5x10-3
1.6x10-2

hi,m1

(En. 4.14)

1.1x10-2
1.1x10-2
8.8x10-3
8.8x10-3
9.7x10-3
6.5x10-3
6.3x10-3
5.6x10-3
6.9x10-3
6.4x10-3
6.1x10-3
5.8x10-3
7.2x10-3
6.6x10-3
6.2x10-3
6.7x10-3
6.8x10-3
8.2x10-3
7.4x10-3
6.8X10'3
6.2x10-3
7.5x10-3
7.1x10-3
6.7x10-3
6.6X10'3
7.8x10-3
7.1x10-3
1.1x10-2
7.7x10-3
6.6x10-3
6.0x10-3
5.9x10-3
5.5x10-3
6.0x10-3
5.5x10-3

hi

(En. 4.19)

For organic substances in poly(dimethylsiloxane), diffusivities are
typically less than 1X10"5 cm2/s and molar partition coefficients, k,,
are typically less than 100. Consequently, longitudinal band-

broadening in the stationary phase (Equation 4.12) may be neglected
to yield the following solution for 131,53

131,5 = [2/31‘1k1/11+kil2l'1d2‘u1/[hrh(,m] (4-20)

In some applications where very narrow bore columns and high
linear velocity mobile phases are used, the mobile phase components
of band spreading, him, may also be neglected (2). Under these
conditions, the diffusivity of a substance in the stationary phase can be
estimated entirely from experimental data combining Equations 4.19
and 20, after substituting u = L/to and k1: (tn-t0)/to, to yield the

following simple relation:

D1,. = 3.69-d2-(t,.1-t0)/Wi2 (4.2 1)

From Table 4.5, it is apparent that for the experimental
conditions in the present study, band spreading in the mobile phase is
not negligible. Therefore, Equations 4.18 or 4.20 are applicable to the
current work. Within three significant figures, identical results are
obtained for calculations using Equations 4.18 and 4.20, indicating
that thl is negligible. Values for Di,s determined for the membrane
and the chromatographic phase, using Equation 4.20, are provided in
Table 4.6. The diffusivities in the membrane for compounds that

exhibit hydrogen bonding are lower when compared with the data for

96

Table 4.6. Diflirsivities at 25 °C in the stationary phase for
compounds of interest determined by membrane extraction

experiments (ME), and gas chromatographic experiments (GC).

compound
pentane

hexane

heptane

benzene

toluene
ethylbenzene
chlorobenzene
chloromethane
dichloromethane
chloroform
carbon tetrachloride
chloroethene

1 , 1 -dichloroethene
trichloroethene
tetrachloroethene
bromomethane
dibromomethane
bromoform

water

methanol

ethanol

1 -propanol
2-propanol
l-butanol

acetone
2-butanone

97

m
4.4x10-6
3.6x10-6
3.2x10-6
4.8x10-6
3.6x10-6
1.7x10-6
1.8x10-6
1.1x10-5
8.0x10-6
4.8x10-6
2.9x10-6
9.0x10-6
5.9x10-6
3.8x10-6
2.3x10-6
9.0x10-6
4.2x10-6
1.3x10-6
2.5x10-6
4.2x10-7
4.0X10-7
4.6x10-7
3.2x10-7
4.8x10-7
5.0x10-7
8.6X10-7

GC E n. 4.20

2.7x10-6
2.9x10-6
3.1x10-6
2.9x10-6
3.6x10-6
6.9X10'7
1.7x10-6
2.2x10-6
4.8x10-6
3.6x10-6
2.3x10-6
1.1x10-6
3.6x10-6
3.3x10-6
1.7x10-6
1.7x10-6
5.3x10-6
1.3x10-6
2.3x10-6
2.9x10-6
3.1x10-6
1.2x10-6
5.1x10-6
1.0x10-6
5.1x10-6
4.1X10-6

the GC stationary phase. This effect is due to adsorption of these
compounds on the silica in the membrane. This adsorption results in
decreased diffusive transport, as described below. While the
treatment resulting in Equation 4.21 will be discussed again,
calculations from the more rigorous Equation 4.20 will be used in the

correlations with membrane extraction data.

Diffusivities increase with increasing temperatures, as illustrated
in Figure 4.3 for diffusivities for selected compounds in the membrane
vs. temperature. This effect results in narrower chromatographic
bands for GC analyses and faster response to steady state in membrane
extraction analyses. The effect of temperature on diffusivity is
described by the Arrhenius relation

3(lnID1,sl)/8(1/T) = -ED./R (4.22)

where ED, is the energy of activation for diffusion. The activation

energies for diffusion for selected compounds were obtained and are
presented in Table 4.7. The activation energies for diffusion are
always positive so that diffusion increases with increasing temperature.
As stated above, because the diffusivities increase with increasing
temperatures, the measurements of tfl and W1 by GC were made with
less reliability at temperatures higher than 25 °C. The diffusivity in
the membrane for l-butanol and other strong hydrogen-bonding
substances are decreased relative to the other compounds when

compared with the data for the GC stationary phase (Table 4.7). This

98

_L

N
1
l

 

 

 

o 10 --
o
m
2
o 8 "
‘9
$3 6 --
><
>1
3: 4 .- X
> -
a X
a 2 d—
0 i i i i i
0 20 40 60 80 100

Temperature, °C

KW:

X = carbon tetrachloride
square = l-butanol
diamond = chlorobenzene

triangle = toluene

Figure 4.3. The efl'ect of temperature on difiusivity, Di... in the ME
stationary phase.

is a result of the adsorption of the hydrogen-bonding substances on

the silica in the membrane.

Table 4.7. Values for the activation energies for difiusion for
selected compounds in the membrane stationary phase.

ED, (kJ (mole)

compound ME
nitrogen 1 6
heptane 1 5
toluene 1 7
chlorobenzene 23
carbon tetrachloride 14
1-butanol 30

In the free-volume theory of diffusion (21), diffusive transport of
a substance in an unfilled, rubbery polymer is related to the molar
volume of the substance as described in Chapter 3. This relationship

can be expressed as follows:
Di.p = Do,p0exp{[-0/(R’1‘)]-v11/3} (4.23)

where Di.p is the diffusivity of component i in the polymeric
membrane, the pre-exponential term, D04), is the diffusivity of some
hypothetical substance with zero molar volume, and 0 is a constant
that is related to the free-volume and the cohesive energt density of
the polymer. In addition, the boiling points of a homologous series of

weak or non hydrogen bonding compounds display a direct

100

relationship with molecular diameter and, therefore, with v11/3.

Consequently, a useful correlation may be obtained from a plot of

ln(1/D,'S) vs. Tbi’ as shown in Figure 4.4. The solution to the curve in

Figure 4.4a for the compounds that exhibit weak or non hydrogen
bonding shows a slope of 6.96X10"3 and an intercept of 10. 1. Because
of the inability to determine the diffusivities of the compounds with
low boiling points (i.e., the poorly retained compounds) by the
chromatographic method, the line plotted in Figure 4.4b was obtained
from the ME data. The diffusion selectivity with the silicone

membrane may be estimated from

D1,S/DJ,S = CXP{6.96X10'3.(Tbj‘Tb1)} (4.24)

Again, the effect of silica on the transport of the strong hydrogen
bonding substances is observed in the ME measurements. The silica
inhibits the diffusive transport of these substances in a process akin to
frontal or integral chromatography (22). This retention process is
described in Chapter 3 by the following relation:

Dl,p/D1,S = 1+k'1 (4.25)

which is derived from the definition of chromatographic retention
(23).

tr/t0 = 1+k'i (4.26)

and the solution for determining diffusion in a membrane (24),

101

16.0

15.0

14.0

13.0

Diffusivity

12.0

11.0

Natural Log of the Inverse of

10.0

16.0

15.0

14.0

13.0

Diiiusivity

12.0

11.0

Natural Log of the Inverse of

10.0

Key:

(8)

 

 

 

 

 

 

1 )-
50 150 250 350 450
Boiling Point Temperature, °C
(b)
It I-
J .
50 150 250 350 450

Boiling Point Temperature, °C

Square = weak or non-hydrogen bonding compound
Circle = strong hydrogen bonding compound

Figure 4.4. The correlation of difl‘usivity, Dis, with boiling point.
Tm, at 25 °C. obtained by ME (a) and by GC (b).

102

01.3 = 0.14-c12/t50 (4.27)

where DLS is the diffusive transport that is observed with retention by
the silica phase, Di'p is the diffusivity through the polymer phase in

the absence of a retentive phase, k'i is the molar partition coefficient

for compound i at equilibrium between the silica and polymer phases,
and t5o is the time required to achieve 50 % steady state permeation

following a step change in concentration in the mobile phase. The
diffusivity of substance in polymers containing fillers have also been
shown to be effected by the tortuous path the substances must travel
(25) so that the relation describing the effect of a filler on diffusive
transport is given by

131,8 = Dl’p/[l'i‘k'd’ll'i'kpf/Z“ (4.28)

where (bf is the volume fraction of the filler in the stationary phase. In

the case of the silicone elastomer, (bf = 0.25. It is easily seen that for

the chromatographic stationary phase (or for an unfilled membrane),
the values for k'i and <I>f are zero so that Di,s = Di.p° By combining

Equations 4.23 and 4.28, the following general solution to the
retention-modified diffusion process is obtained:

D(,s = Do,p'eXp{[-@/ (RT)l°V(1/3}/{[1+k'gl'[1+(<1>f/ 21]} (4.29)

The constant values Dop, 9, and (bf have been determined

experimentally (Chapter 3) to yield the following solution for
diffusivities in the silicone elastomer at 25 °C:

103

D1,. = 8.25X10'40exp{-1.060v11/3}/[1 + k',] (4.30)

It is believed that the forces that govern separations by liquid-
solid chromatography (26, 27) also govern this retention and would
therefore depend upon the nature of both the polymer phase and the
filler phase. For describing the process of a substance partitioning
between a permeable mobile phase and an impermeable stationary
phase, i.e., adsorption, the molar area, rather than the molar volume of
the partitioning substance is typically used (6-9, 15). In liquid-solid
chromatography, the thermodynamic description has been presented
as a linear relationship between energr of adsorption and the square of
the solubility parameter (15). Similarly, the following relationship has
been shown in Chapter 3 to describe the process of adsorption of a
substance onto a silica filler from a poly(dimethylsiloxane) phase:

ln(k'l) = Inwf/vp) + [viz/3/(RT)][A-512 + B] (4.31)

where the filler/ polymer volume phase ratio, Vf/Vp, is known to be

0.33, and the constants A and B have been experimentally determined
in Chapter 3. With these values, and combining Equations 4.29 and
4.30, the following solution to the diffusion-partition process is given:

DLS = 8.25X10'40expl-1.060v11/ 3}
/(1 + 0.33-exp([v,2/3/(RT))-[13.4-5,2 - 5591)) (4.32)

Presented in Table 4.8 are the diffusion selectivity, D1,s/ D] /S, values

predicted from this equation and from the boiling point model

104

Table 4.8. Difiusion selectivities for compounds over nitrogen and

over heptane at 25 °C. Tb = predicted from boiling point model
(Equation 4.24); SP = predicted from solubility parameter theory

(Equation 4.31); ME as experimental from ME data: G0 =

 

 

 

experimental from GC data.

relative to nitrogen relative to he otane
minimise lb 3 ME Tb S1” 143 Q:
nitrogen 1.0 1.0 1.0 6.7 9.1 6.6 -
oxygen 0.91 1.0 1.0 6.2 8.8 6.6 -
argon 0.93 0.50 1.0 6.3 4.5 6.6 -
carbon dioxide 0.44 0.51 0.62 3.1 4.7 4.1 -
methane 0.80 0.55 0.76 5.4 5.0 5.0 -
ethene 0.52 0.40 0.52 3.7 3.7 3.4 -
ethane 0.47 0.36 0.52 3.3 3.3 3.4 -
propane 0.34 0.25 0.30 2.5 2.3 2.0 -
butane 0.26 0.21 0.30 1.9 1.9 2.0 -
pentane 0.20 0.16 0.21 1.5 1.5 1.4 0.88
hexane 0.16 0.13 0.17 1.2 1 .2 1 .1 0.93
heptane 0.13 0.11 0.15 1.0 1.0 1.0 1.0
benzene 0.15 0.16 0.23 1.1 1.5 1.5 1 .0
toluene 0.12 0.14 0.17 0.92 1.2 1.1 1 .1
ethylbenzene 9.9X10'2 0.1 1 8, 1x10'2 0.78 1 .0 0.53 0.22
chlorobenzene 0.10 0.1 1 8.6X10'2 0.80 1.0 0.56 0.56
chloromethane 0.30 0.30 0.52 2.1 2.7 3.4 0.70
dichloromethane 0.19 0.23 0.38 1.5 2.1 2.5 1 .6
chloroform 0.17 0.19 0.23 1.1 1.7 1.5 1.2
carbon
tetrachloride 0.15 0.18 0.14 0.91 1.6 0.83 0.73
chloroethene 0.28 0.34 0.43 2. 1 3. 1 2.8 0.37
1,1-dichloroethene 0.20 0.21 0.28 1.5 1.9 1.8 1.2
trichloroethene 0. 14 0. 16 0.18 1.1 l .5 1.2 1.1
tetrachloroethene 0.1 1 0.12 0.1 1 0.72 1.1 0.75 0.54
bromomethane 0.25 0.30 0.43 1.8 2.8 2.8 0.56
dibromomethane 0.13 3.9x10-2 0.20 1.0 0.31 1.3 1.7
bromoform 9.0x10-2 5.3x10-2 6.2x10-2 0.72 0.53 0.41 0.40
water 0.13 2.3x10-4 0.12 0.99 2.1x1o-3 0.73 0.74
methanol 0.16 1.5x10-2 2.0xro-2 1.2 0.14 0.13 0.93
ethanol 0.15 2.4x10-2 1.9x10-2 1.1 0.22 0.13 0.99
1-propanol 0.13 2.4x10-2 2.2x10-2 1.0 0.22 0.15 0.39
2-propanol 0.14 3.9x10-2 1.5x10-2 1.1 0.36 0.10 1.6
l-butanol 0.11 2.1x10-2 2.3x10-2 0.39 0.19 0.16 0.32
acetone 0.17 0.16 2,4X10‘2 1.3 1.4 0.16 1 .7
2-butanone 0.15 0. 15 4.1X10'2 1.1 1.4 0.27 1.3

105

(Equation 4.24) for selective diffusion over nitrogen and heptane for
the compounds studied. Again, the boiling point model exhibits the
poorest correlation with the ME data for the strong hydrogen bonding
compounds. The boiling point model typically predicts relative
diffusivities that are five to ten times higher than observed by ME for
these compounds. On the other hand, this model yields good
correlation with the GC data. The solubility parameter model for the
membrane considers the effect of the silica on the diffusive transport
and yields a very good correlation for most of the compounds. The
compounds that yield low distribution ratios for the GC stationary
phase yield the poorest correlation between the GC and ME data
because of the inability to accurately measure the widths of these GC

bands as discussed above.

Just as with the distribution ratio selectivities, the diffusion
selectivities may be modeled by the chromatographic process. For the
best correlation, both the GC and the ME phases should be identical,
since the presence of polymer additives and fillers may significantly
affect the thermodynamic and kinetic transport properties. As
demonstrated, the presence of such additives and fillers may be taken

into account using known chromatographic principles.

EFFICIENCY AND ENRICHMENT

Since the permeation enrichment factor, 81/] = (Di,s/ DJ.S)(K1/ K1).

is comprised of parameters that have been characterized by solubility

parameter theory, then the enrichment factor may be modeled by

106

combining Equation 4.3 for the distribution ratio with Equation 4.32
for the diffusivity.

From chromatography, the distribution selectivity may be
written as

KI/Kj = kI/kj = (tri‘to)/(trj'to) (4.33)

and from Equation 4.20, after substituting u = L/to and k1: (tn-tO)/to,

the diffusion selectivity may be written as
D1,s/Dj,s = [ltn'tol/(trj'toll'ltrj/tr1]2‘[(hj‘hj,m)/(hi-111,31” (434)

Therefore, the relationship between the permeation enrichment

factor, 81/] = (D1,s/Dj,s)(K1/Kj). and chromatographic measurements

may be written as follows:

(3,,J = ((tn-toi/(tn-tonz-(tn/tnIZ-uhj-hjm)/(h.-h.,m)1 (4.35)

If ideal conditions prevail, where the band spreading in the mobile
phase is negligible, then Equation 4.21 is used to determine
diffusivities so that the relationship between the permeation

enrichment factor and chromatographic measurements is given by:

8U} = [WJ/WilZ'th-to)/(trj-to)12 (4.36)

107

Since the chromatographic effective theoretical plate number

for component i is defined as (19)

N1 = 5.54.[(tr1-t0)/W1]2 (4.37)

The resulting relationship between 8 and N can be expressed as

The effect of temperature on the enrichment factor is given by

where AEp is the difference in activation energr for permeation

between compounds 1 and j, given by AEp = Epi'Epj. Values of Ep, for

selected compounds in the silicone elastomer are given in Table 4.9.

Table 4.9. Values for the activation energies for permeation for
selected compounds in the membrane stationary phase.

E131 lkJ (mole!
compound _M_E_
nitrogen 8
heptane - 12
toluene - l 7
chlorobenzene -25
carbon tetrachloride — 17
l-butanol — 16

108

The activation energr for permeation is in fact the sum of the
heat of solution and the activation energy for diffusion. In the case of
the silicone stationary phases, the heats of solution for most organic
compounds are greater in magnitude than their activation energies for
diffusion, therefore an increase in temperature results in a reduced
permeability. The plots of 1n(P1) vs. temperature in Figure 4.5
demonstrate the dominance of the distribution ratio in the effect that
temperature has on the permeation of organic compounds in the
silicone materials. For gases such as nitrogen and oxygen, the
activation energies for diffusion dominate so that their permeabilities
increase with increasing temperature. The result is that as the
temperature increases, the enrichment factor for the organic
compounds over nitrogen (and air) decreases. Since measurements of
the chromatographic band widths at temperatures above 25 °C were

not reliable, these data are not shown.

The plot of ln[8(1/N2)] vs. Tbi shown in Figure 4.6 illustrates the

dominance that the distribution ratio exhibits for the permeation
process. The correlation between enrichment factor and boiling point

for the non— and weakly hydrogen bonding compounds is given by

81/] = exp{2.15X10'20(Tb1-Tbj)} (4.40)

which is the product of Equations 4.7 and 4.24. The hydrogen
bonding compounds show a reasonable correlation with the line

plotted for the compounds that exhibit weak or no hydrogen bonding.

109

3500 --

2500 ~-

2000 --

1500 --

1000 --

Permeability, X10-6 cm2/sec

500 a...

 

Key:

X = carbon tetrachloride
square = l-butanol
diamond = chlorobenzene
triangle = toluene.

Temperature, °C

 

Figure 4.5. The efiect of temperature on permeability, P1, in the

ME stationary phase.

110

 

 

 

8.50 "

_ 7.50

(D

>

O 6.50
E

E 5.50
S

Q

If] a 4.50
w 2

5 t: 3.50
.. 2

O

03 2.50
3

'3 1.50

3

E

Z 0.50

-0.50 i i t i
50 150 250 350 450

Boiling Point Temperature, °C

Key:
square = weak or non-hydrogen bonding compound
circle = strong hydrogen bonding compound

Figure 4.6. The correlation of enrichment factor (over nitrogen),
81mg. with boiling point. Tm. for data obtained by ME at 25 °C.

111

This improved correlation may be due to the inhibited diffusion from
the silica being offset by enhanced partitioning.

The enrichment factors over nitrogen and over heptane are
presented in Table 4.10 for the boiling point and solubility parameter
models as well as the ME and Ni/Nj data. The solubility parameter
model showed good correlation with the ME data for the enrichment
of the compounds over nitrogen. Only for pentane, hexane, heptane,
2-propanol, and 1-butanol do the values predicted from this model
deviate significantly from the experimental data. Many of the values
for the selectivity over heptane again showed deviation from the
experimental values using this solubility parameter model. In general,
the correlation between the ME and GC enrichment factors was quite

good.

FURTHER CONSIDERATIONS

The results described in this chapter suggest that
chromatographic data may be the basis for a simple and practical
method for selecting a membrane for a specific separation application.
In general, if two components are readily separated by
chromatography, then they will be readily separated by a membrane
composed of the chromatographic stationary phase. The distribution
ratios for compounds between the stationary and mobile phases will be
linear with the chromatographic retention times, while the
diffusivities will roughly be inversely proportional to the retention
times. The implication of this "rule-of-thumb" to an analysis is that the

112

Table 4.10. Enrichment factors for compounds over nitrogen and

heptane at 25 °C. Tb = predicted from the boiling point model

(Equation 4.40); SP = predicted from solubility parameter theory
(Equations 4.3 and 4.32); ME = experimental from ME data (Pi/P1);

GC = experimental from GC data (Equation 4.35).

commund
nitrogen

oxygen

argon

carbon dioxide
methane

ethene

ethane

propane

butane

pentane

hexane

heptane

benzene

toluene
ethylbenzene
chlorobenzene
chloromethane
dichloromethane
chloroform
carbon
tetrachloride
chloroethene

l , 1 -dichloroethene
trichloroethene
tetrachloroethene
bromomethane
dibromomethane
bromoform
water

methanol
ethanol

1 -propanol
2-propanol

1 -butanol
acetone
2-butanone

relative to nitrogen

relative to heptane

 

It;

1700

270

370

§_P

120

1700
0.37

320
1 100
l 100
3200

650

MB.
1.0
1.9

 

l‘b

1.8x1o-3
2.4x10-3
2.2x10-3
2.2x10-2
3.5x10-2
1.3x1o-2
1.8x1o-2

113

_s_p
4.1x1o-3
9.0x1o-3
1.2x10-2
2.3x1o-2
1.7x1o-2
4.4x10-2
4.5x1o-2
5.1x10-2
9.1x1o-2
0.17

M_E
1.2x10-3
2.3x10-3
2.3x1o-3
1.5x1o-2
5.6x10-3
1.4x10-2
1.5x10-2
3.6x10-2
4.4x10-2
0.31

0.39

l8

more permeable a compound is, the longer is its response time.
These principles are illustrated in the gas chromatogram and the

permeation parameters given in Figure 4.7.

In addition to gas analysis, analytical ME techniques are also
commonly used for the analysis of aqueous samples. The same
principles described above may be applied to these separations. In the
case of compounds that exhibit weak or no hydrogen bonding, the
compounds with the lower boiling points exhibit higher enrichment
factors over water because of their low solubility in the water as shown
in Chapter 2. The strong hydrogen bonding compounds partition
poorly into the membrane from an aqueous matrix, which results in

low permeabilities.

114

GC

 

bromoform
ethylbenzen

H

16:60

cl

 

 

 

 

8
.3
chlorobenzene "'
8
tetrachloroethene §
3
toluene '3
heptane
trichloroethene g
dibromomethane '3
carbon tetrachlonde benzene
chloroform
dichloroethene
pentane .
nrtrogen

 

 

 

 

 

1600

1400

 

E/N2

.2400
1500

L14oo

 

1600

 

Figure 4.7. The correlation of GC retention times with ME

permeation parameters at 25 °C.

115

 

GC

 

bromoform
ethylbenzen

q

16860

;

 

 

 

 

 

    
  

8
3
chlorobenzene "'
3
tetrachloroethene §
3
toluene "'3

heptane
trichloroethene g
dibromomethane __.. -;

carbon tetrachloride
benzene
chloroform
dichloroethene
pentane

 

 

 

 

 

1900

1600

1400

L580

 

530
370

320
10

180

 

 

 

E/N2

_2400
_1 500

L1...

1600

 

 

 

Figure 4.7. The correlation of GC retention times with ME

permeation parameters at 25 °C.

115

 

REFERENCES

(l)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Braun, J.-M.; Guillet, J. E. Adv. Polym Sci. 1976, 21, 107.

Lloyd, D. R.; Ward, T. C.; Schreiber, H. P., eds. Inverse Gas
Qhromatogmphy, ACS Symposium Series; American Chemical
Society: Washington D.C., 1989.

LaPack, M. A.; Tou, J. C.; Enke, C. G. AnaL Chem 1990, 62,
1265.

Fjeldsted, J. C. Instrument Society of America International
Conference and Exhibition, New Orleans, IA, 1990.

Mears, P. In: Membrane Separation Processes; Mears, P., Ed.;
Elsevier: Amsterdam, Netherlands, 1976.

Hildebrand, J. H.; Scott, R. L. The Solubiligg of Nonelectrolfles,
3rd Ed.; Reinhold: New York, NY, 1950.

Hansen, C.; Beerbower, A. Solubility Parameters, In Kirk-

Othmer Engclopedia of Chemical Technology, Suppl. Vol., 2nd.
Ed.; 1971.

Barton, A. F. M. Handbook of Solubility Parameters and cher
Cohesion Parameters; CRC Press, Inc.: Baco Raton, FL, 1983

Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regplar and
Related Solutions VanNostrand-Rheinhold: Princeton, NJ , 1970.

 

Prausnitz, J. M.; Shair, F. H. A.I.Ch.E. J. 1961, 7, 682.

Weast, R. C., ed. Handbook of Chemist__1;y and Physics,64th Ed.;
CRC Press, Inc.: Baco Raton, 1983.

Jennings, W. Gas Chromatography with Glass Capillm Columns,
2nd Ed.; Academic Press: New York, NY, 1980.

116

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

Bermejo, J .; Guillen, M.D. Chromatographia 1983, 17, 664.

Karger, B. L.; Snyder, L. R.; Horvath, C. An Introduction to
Separation Science; Wiley-Interscience: New York, NY, 1973.

Karger, B. L.; Snyder, L. R.; Eon, C. AnaL Chem. 1978, 50, 2126.

Van Deempter, J. J .; Zuiderweg, F. J .; Klikenberg, A. Chem Eng.
Sci. 1956. 5. 271.

Golay, M. J. E. In: Gas Chromatoggaphy 1957: East Lansing
Symposium, Coates, V. J .; Noebels, H. J .; Fagerson, I. S., Eds.;
Academic Press: New York, NY, 1958.

Fuller, E. N.; Schettler, P. D.; Giddings, J. C. Ind. Eng. Chem.
1966. 58. 19.

Desty, D. H.; Goldup, A.; Swanton, W. T. In: Gas Chromatoggphy,
Brenner, N; Callen, J. E.; Weiss, M. D., Eds.; Academic Press:
New York, NY, 1962.

Holland, J. F.; Enke, C. G.; Allison, J .; Stults, J. T.; Pinkston, J.
D.; Newcome, B.; Watson, J. T. AnaL Chem. 1983, 55, 997A.

Brandt, W. W. J. Phys. Chem., Wash.., 1959, 63, 1080.

Grob, R. L. Modern Practices of Gas Chromatoggaphy; Wiley-
Interscience: New York. NY; 1977.

Giddings, J. C. Dypamics of Chromatoggaphy, Vol. 1; Marcel
Dekker: New York, NY; 1965.

Ziegel, K. D.; Frensdorff, H. K.; Blair, D. E. J. Polym. Sci. 1969.
7. 809.

van Amerongen, G. J. Rubber Chem. TechnoL 1964, 37, 1065.

117

(26) Snyder, L. R. Principles of Adsogption Chromatoggaphy; Marcel
Dekker: New York, NY; 1968.

(27) Kirkland, J. J ., (Ed.) Modern Practice of Liquid
Chromatogaphy; Wiley-Interscience: New York, NY; 1971.

118

CHAPTER 5

Practical Aspects of Membrane Extractions

 

In this chapter, practical aspects for optimizing experimental
and instrumental parameters are discussed for membrane extraction
mass spectrometry. Some experimental conditions that affect
membrane extraction efficiencies include temperature and sample
flow rate. The experimental conditions under which an analysis of a
chemical process is performed are often dictated by the process itself.
The instrumental parameters that may be more easily controlled
include the membrane dimensions, the ME device configuration, and
the distance between the membrane extractor and the analyzer.
Another concem for the analyst is the potential for a thin-walled
membranes to rupture, allowing the sample or process stream to vent
the mass spectrometer. This is of particular concern in process
applications where many process streams are complex and the

membrane may degrade by physical, chemical, or thermal means.

A variety of devices for ME have been developed to separate
compounds of interest from a sample matrix and introduce these
compounds into a mass spectrometer. Hollow fiber or tube
membranes have seen a great deal of use in ME-MS applications (1-7).
Several groups have also devised systems for making sheet ME-MS

interfaces (7 -10). More recently, hollow fiber and sheet membrane

119

extractors have been incorporated directly into the vacuum chamber
and even the ion source of the mass spectrometer with the goal of

improving the sensitivities and response times (11- 13).

TWO hollow fiber membrane extractor configurations have been
reported and contrasted. The flow-through device for ME is
configured such that sample flows through the interior of the hollow
fiber membrane while the analytes permeate radially to the outside,
where they are analyzed. Conversely, the flow-over device for ME is
configured such that the outside of the hollow fiber membrane is
exposed to the sample while the inside is exposed to the MS vacuum.
Basic designs for flow-over and the flow—through hollow fiber

membrane extractors are illustrated in Figures 5.1 and 5.2.

The following points are important experimental considerations
for on-line ME—MS techniques:
1) Experimental control is desired over parameters that affect
permeability or that may damage the membrane, such as the
membrane temperature and linear velocity of the sample.
2) The membrane should be protected from being torn due to
pinching or abrasion.
3) In the event of a ruptured membrane, the analyzer should
irmnediately be isolated from the ME device so that the mass
spectrometer is not vented by the sample.
4) The surface area and void volume of the ME-MS interface should
be minimized. Interface tubing, fittings, vacuum-protection valves,

120

to
sample pump

L X X X ‘ ‘ I '

sxxxx

hollow fiber
membrane

sealant

‘XXX“‘11‘LJX“‘X““V

   

‘

 

‘A‘X‘XUX‘X‘

 

 

 

 

 

. .

 

 

l1‘L11“11“t

 

 

txxxxlII‘Kxxxxj

 

 

 

 

 

10 mass

permeate spectrometer

Figure 5. 1 . Flow-over hollow fiber membrane extractor.

121

to
sample pump

‘lIIl‘x‘

hollow fiber
membrane

sealant

 

\X‘Ll“‘r‘j““jl““

 

 

Vi

 

 

 

 

sample

111XXifiK111I

 

 

mixxxxxix“

 

 

 

 

 

to mass

pe rmeate spectrometer

Figure 5. 1. Flow-over hollow fiber membrane extractor.

121

to
sample pump

 

hollow fiber

membrane

014/,
”fix\\\

 

 

"1------1.

 

 

 

  

  

to mass
spectrometer

     

                

>

 

permeate

 

 

 

 

"AF1FA“”’"‘HIH

g

sample

 

 

 

t
n
.B
a
e
S

Figure 5.2. Flow-through hollow fiber membrane configuration.

122

and the ME device contribute to the surface area and void volume in
the ME-MS interface.

5) In processes where highly reactive analytes or reaction kinetics
are to be measured, the shortest distance possible between the sample
and the membrane extractor is desired to minimize loss of the analyte
or skewing of the reaction profile.

6) In some applications, it is desirable to monitor multiple streams
of gas and liquid process streams, as discussed in Chapter 6, thus

more than one ME device may be required.

Several experimental parameters are discussed below in the

context of optimizing the analytical speed, sensitivity, and selectivity.

MEMBRANE DIMENSION CONSIDERATIONS

The permeation equations discussed in Chapter 2 show that the
permeation rate increases, and therefore the detection limit
decreases, as a function of sheet membrane area or hollow fiber
membrane length. In the case of the hollow fiber membrane, the
permeation rate for the analyte increases with increasing length only
to the limit Where the concentration of the analyte in the sample does
not change along the hollow fiber due to efficient extraction into the
membrane (14, 15). In such cases, it is preferred that the membrane
extractor be constructed with several short hollow fiber membranes,
rather than with a single long one to ensure uniform sample

concentration along the membrane surface.

123

The amount of analyte removed by the permeation process per
unit length of membrane is actually quite small as illustrated by the
permeation rates per unit concentration through a silicone hollow
fiber membrane given in Table 5.1 for several gas phase compounds.
By pumping a water sample from a 48-cc volatile organic analysis
(VOA) vial through the membrane and back into the vial, small samples
have been analyzed without appreciable consumption of the sample
and without formation of headspace in the vial. A water sample spiked
with toluene and dichloromethane was pumped at various rates
through three flow-through hollow fiber membrane extractors in
series and their permeate streams were analyzed. No significant drop
in permeation rate between the first and the third membrane in the

series was observed.

The detection limit for an analyte is proportional to the
thiclmess of a sheet membrane. In the case of hollow fiber
membranes, the following treatment may be useful in understanding
the permeation rate-hollow fiber wall thickness relationship. In
Chapter 2, it was shown that the permeation rate through a hollow

fiber membrane is given by

F, = 2°n0L°P1°cmi/ln(o.d./i.d.) (5. 1)

Since o.d./i.d. = outer radius (o.r.)/inner radius (i.r.), and since (1 = or

- i.r., then Equation 5.1 can be written as

F; = 2-rr-L0P10cmi/lnu + d/i.r.) (5-2)

124

Table 5. 1. Gas permeabilities and permeation rates / unit

concentration (given per unit ppm by volume) through a 2.54-cm-

long, 0.0305-cm-i.d., 0.0635-cm-o.d. silicone hollow fiber

membrane.

permeability
9.0mm Il_0 Sawmill
nitrogen 2.1
oxygen 4.0
argon 4.0
carbon dioxide 2 5
ethene 24
methane 9. 7
ethane 2 5
propane 6 1
butane 7 6
pentane 53 0
hexane 670
heptane l 700
benzene l 000
toluene 2000
ethylbenzene 3200
chlorobenzene 3000
chloromethane l 40
dichloromethane 740
chloroform 900
carbon tetrachloride 920
chloroethene 1 20
1 , 1 -dichloroethene 600
trichloroethene 1 400
tetrachloroethene 3 500
bromomethane l 40
dibromomethane l 200
bromoform 5 1 00
methanol 400
ethanol 840
l -propanol l 000
2-propanol 2 7O
1 -butanol 1 1 00
acetone 540
2-butanone l 300
water 8 7

125

permeation rate

LQ'10c_,m3[ISOppm ||

1100

180
220

58
240
120
280

19

Therefore, a reduction of the thickness / inner radius ratio for a hollow
fiber membrane results in an increase in permeation rates and thus an

improvement in the detection limits.

In addition to improved detection limits, faster response times
are achieved with thinner membranes. The membrane thickness-
response time relationship given by Equation 2.13 shows the response
time to be directly proportional to the square of the thickness for both
the sheet and the hollow fiber membranes. As stated above, a concern
for mass spectrometrists is the potential for the thin-walled
membranes to rupture, allowing the sample or process stream to vent
the mass spectrometer. In many cases, the polymer membrane is
sufficiently strong that leaks are more likely to occur at the sealant
used to attach the membrane to the ME device.

Because the enrichment factor is given by the ratio of the
permeabilities for two components in a sample, it is not affected by
the dimensions of the membrane. Therefore, utilizing membranes
that have thinner walls or larger surface areas will improve the speed
and sensitivity, but not the selectivity.

TEMPERATURE CONSIDERATIONS

As described in the previous chapters, the permeation rates for
organic compounds from gas phase samples are dominated by the
membrane/ gas distribution ratio. Because their permeabilities

decrease with increasing temperatures. their detection limits increase

126

(see Table 2.2). The effect of temperature on the permeabilities for
organic compounds from water appears to be diffusion-dominated,
therefore at higher temperatures, their detection limits improve.
Higher temperatures result in increased diffusivities and therefore
shorter response times. However, enrichment factors degrade at
higher temperatures. In addition, for trace level organic samples, the
analyzer pressure follows the permeabilities of the air or water matrix.
Therefore. lower temperatures are desired for lower analyzer
pressures and to minimize oxygen and water in the mass

spectrometer.

For the most efficient membrane extractions, altering the
membrane dimensions rather than increasing the temperature is
generally better for obtaining improved detection limits and response
times. But the choice of membrane thickness is limited to
commercial availability or the capability to cast thin, supported
membranes that will withstand the pressure differential imposed by
the sample and mass spectrometer. With a given membrane, the
desire for increased sensitivity and reduced response time must be
balanced with the need for efficient separations. Higher temperatures
may be warranted for kinetic studies requiring fast response.
Processes have been studied at temperatures exceeding 100 °C (16)
and performance evaluations have been carried out at temperatures
greater than 200 °C (17). The membrane material is rated for a
workable temperature range of -54 °C to 249 °C (18). However, the
lifetime of the membrane is expected to be reduced at elevated

temperatures. At room temperatures, the Silastic material has a

127

reported shelf-life (for medical uses) of 5 years. The operating
lifetime will depend upon the conditions of the application.

SAMPLE FLOW RATE CONSIDERATIONS

Poor mixing at the sample/ membrane interface can cause the
formation of a layer of analyte depletion, resulting in low response.
This phenomenon is commonly reported by the users of flat
membranes (19, 20). The effect of the boundary layer is depicted in
Figure 5.3 where the permeation rate is now given by

F1 = A‘P1.Cmi./d (5. 3)

The reduced concentration of analyte i, cmi‘, at the interface of

the boundary layer and the membrane now establishes the
concentration gradient in the membrane. Turbulent flow is preferred,
particularly for water samples where the rate of diffusion through the
membrane may be greater than through water for many compounds.
The transition from laminar flow to turbulent flow occurs at Reynolds
number values of 2000-3000 (21),

NRC = i.d.-v-p/p. (54)

where v is the sample linear velocity, p is the density of the fluid, and
u is the fluid viscosity. To achieve these values however, volume flows
of over 25 cm3/minute for water (25 °C) are required in a 0.0305-cm

i.d. hollow fiber membrane.

128

membrane

(stationary phase)
sample or ' d "
feed stream extract or
(mobile phase) permeate stream

 

‘ F = A-D-K-cde

r

 

 

 

Figure 5.3. A cross-section view of the effect of boundary layers on
the permeation process.

129

100

 

 

 

 

E 90
“E 80
3
3' 70
g 60
E 50
3
40
3
c 30
o
n- 20
m
o
r: 10
0 . 4. i l ‘ l
0.0 2.0 4.0 6.0 8.0 10.0
Flow Rate, cclmin.
O 200 400 600 800

Reynolds Number

Figure 5.4. Response for toluene vs. sample flow rate through a 2.5-
cm-long, 0.0305-cm i.d.. 0.0635-cm o.d. hollow fiber.

130

The effect of linear velocity on response for toluene in water is
shown in Figure 5.4. Flow rates approaching 10 cm3 / minute appear to
reduce the boundary layer to dimensions where the change in
permeation rate with change in sample flow rate becomes small for
most volatile organic analytes studied. When drawing the sample
through the 0.0305-cm i.d. hollow fiber by pumping at the outlet, flow
rates higher than 10 cm3/minute often result in the formation of
bubbles in the sample stream. To avoid undue pressurization of the
membrane, samples are generally not pushed through the membrane
by the sample pump. Increased turbulence (and thus permeation
rates) for a given flow rate have been achieved by segmenting the flow
stream (22) and packing the interior of the hollow fiber membrane
with inert beads (23). These techniques have not been employed in
this work.

The observed increases in organic permeation rates from water
with increasing temperature may in part be due to the fact that the
Reynolds number increases with temperature according to the
relation NRe = d-v-(O.OO538°T2 + 2.380T + 48.7) so that boundary
layers are reduced at higher temperatures. This relation was
determined from curve-fitting a plot of water density/viscosity ratios

(24) vs. temperature.

In addition to reduced steady state response, poor mixing also
results in longer response times due to the additional boundary layer
through which the analyte must diffuse. Increasing the water flow rate

through the hollow fiber from 1.3 cm3/ minute to 3.5 cm3/ minute

131

results in an approximately 50% decrease in t50 measurements for

both toluene and dichloromethane. This effect on response time is
dependent upon the diffusivity of the substance in the sample matrix
and upon the thickness of the boundary layer. Elimination of this
boundary layer reduces the response time to the limit imposed by the
membrane. For toluene and dichloromethane, response time appear

to become constant at flow rates greater than about 8 cm3 / minute.

When an analyte-depleted boundary layer is established, the
observed enrichment factor is reduced due to the depressed
analyte/ matrix ratio at the sample-membrane interface. A plot of the
analyte/ matrix response ratio vs. flow rate follows the same trend as
that for the analyte response shown in Figure 5.4. The matrix is in
such large excess that changes in its response are relatively small.
When the permeation rates becomes independent of sample flow rate,

so do the organic enrichments.

THE EFFECTS OF DISTANCE BETWEEN THE MEMBRANE
EXTRACTOR AND Tm MASS SPECTROMETER

At least two phenomena associated with the ME-MS interface
tube may result in extended response times and decreased
sensitivities; poor conductance and adsorption. The membrane not
only serves to separate the components of interest from the sample
matrix, but because the flow rate through the membrane is so small, as
shown in Table 5.1, the membrane also provides the necessary

pressure drop from the ambient pressure sample to the high vacuum

132

in the mass spectrometer. For example, the permeabilities and flow
rates through the membrane are given in Table 5.2 for nitrogen,
dichloromethane, toluene, acetone, and l-butanol. The nitrogen is the
sample matrix and approaches 100% concentration. The organic

compounds are 100 ppm by volume in the sample.

Table 5.2. Gas permeabilities and flow rates through a 2.5-cm-long,
0.0305-cm-i.d., 0.0635-cm-o.d. silicone hollow fiber membrane.

 

concentration permeability flow rate
compound % by volume fizflfld fl3&_
nitrogen 100 2. 1X1 0'6 4.6X10'5
dichloromethane 0.01 7.4X10‘4 1.6X10’7
toluene 0.01 2.0X10'3 4.4X10'7
acetone 0.01 5.4X10'4 1.2X10'7
l-butanol 0.01 1. 1X10'3 2.4X10'7

The permeate side of the membrane is under high vacuum,
therefore molecular flow conditions prevail in the interface tube. In
the two-step process of difi'usion through an amorphous polymer
followed by molecular flow through a tube, the diffusion step will be
rate limiting. Since the analytical response for a component is
dependent upon the conductance of the component into the ion
source, then any effect that the interface tubing might have on
conductance would be observed in both the response and the response
time. The data in Table 5.3 for steady state response measurements
for dichloromethane, toluene, acetone, and l-propanol showed no

significant change with the hollow fiber ME device at distances of 40

133

cm, 70 cm, and 100 cm from the ion source. In addition, no change
in the analyzer pressure was observed for the different lengths of

interface tubing.

Table 5.3. The efl'ects of interface tube length on response.

response factor (intensity/ppm)

 

compound ple L=40 cm L=70 cm L: 100 cm
dichloromethane 84 1600 1 600 1 600
toluene 9 1 26000 24000 24000
acetone 58 550 550 550
l-butanol 56 5100 5000 5000

The effect of interface tube length on response times were
examined by making step changes in the sample concentration and
measuring the time required to reach steady state permeation. The
effect of interface tube length on response time for toluene is
illustrated in Figure 5.5. No significant changes in these response
curves are observed. A plot of response time vs. interface tube length
for dichloromethane, toluene, acetone, and l-butanol are shown in
Figure 5.6. Only l-butanol showed a dependency on the tube length as
shown in Figures 5.6 and 5.7. This pronounced dependency on the
interface tube length or, more precisely, on the interface tube surface
area for alcohols has also been reported by Lauritsen (13). In the
present study, this adsorption phenomenon is shown to be minimized
by simply heating the interface tube as demonstrated by the large
square data point in Figure 5.6 and the plot designated d in Figure 5.7.

134

RESPONSE

 

 

 

Figure 5.5. The response curves for m/z 92 following a step change
in the concentration of toluene in a gas sample with difi‘erent
lengths of ME-MS interface tube lengths.

135

350 --

300 '-

250 ~-

200 --

150 --

Response Time, sec.

+

I

‘o

.11. .4.
I I I I I

I

 

 

 

 

50-- .7
I

30 40 50 60 70 80 90 100 110
Interface Tube Length, cm

square = l-butanol

circle = acetone

diamond = toluene

triangle = dichloromethane

large square = l-butanol with the interface tube heated to 150 °C

Figure 5.6. Response time vs. ME-MS interface tube length for
various volatile compomds.

136

 

 

5100* - - -- .U: v—v-rfi‘: —r.

50.:—/

 

 

 

 

 

' 's'o' ' ' '160' ' ' '1§.o' ' ' 'zbo' ' ‘ ‘2‘50‘ ' ' '360' ' ' '3§6 ' ' '466 ’ rflo‘r'

Time, sec.

5

40 cm, 23 °C
70 cm, 23 °C
100 cm, 23 °C
100 cm, 150 °C

Figure 5.7. The response curves for 1-butanol(m/z 56) with
difierent lengths of ME—MS interface tube.

137

As discussed in Chapter 2, the response time for a component is

defined as the time required to reach 50% of the steady state signal,
t50, following a step change in sample concentration at to. It may also

be useful to use an experimental rise time from tlo to tgo to describe

the response time of the membrane extraction technique. For Fickian

behavior, the correlation of t50 to this rise time is approximated by

“904101 = 0-5'1t50'tol (5.5)

If Fickian behavior is not observed (e.g., if adsorption/ desorption of
the analyte on the membrane or analyzer surfaces is the rate limiting
step to attain steady state), then this rise time will yield a misleading
system response time. The rise time measurement is determined
only from the permeate response curve with no reference made to the
sample. Values for the rise time and t50 are given in Table 5.4 for l-
butanol. These data illustrate that the rise time gives no indication of
the system response time and therefore gives no indication when a

change occurs in the sample or process.

Table 5.4. Comparisons between response time (t5o-to) and rise
time (tgo-t 10) for l-butanol.

interface t5040 t90410
tube length seconds seconds
40 cm 75 95

70 cm 180 100
100 cm 340 100
100 cm, 150 °C 80 110

138

Other causes for non-Fickian behavior are common (25-27).
Many rubbery membranes contain fillers such as silica or carbon black
to provide mechanical strength (28). As described in Chapters 3 and
4, the silica has a dramatic effect on the response time for molecules
that exhibit strong hydrogen bonding due to adsorption/ desorption
processes occurring within the membrane. If this
adsorption/ desorption process is reversible, as it appears to be for low
molecular weight compounds, then Fickian behavior is observed.
However, if a very strong interaction occurs between the filler and the
permeating compound, non-Fickian transport would result,
resembling the characteristics of adsorption/ desorption at surfaces
observed in this study.

When transport through the membrane is the rate-limiting step
for the response time (i.e., the membrane is near the ion source or no
interaction of the analyte with the interface surfaces is observed), then
the rise time may yield erroneous values for the system response time.
It would appear that the most useful characterization of response time

should provide a reference to the sample, e.g., t50-t0 or tgo-to (if tgo

can be accurately measured), in addition to the rise time (17).

Another major factor that may affect response time that has not
been addressed in the previous discussion is the effect of the mass
spectrometer. The geometry of the ion source and the vacuum
chamber may have a significant effect upon the response time that is
independent of the membrane extractor and interface tube. The

response time for dichloromethane and toluene are given for three

139

different mass spectrometers in Table 5.5. Whereas the response
time data collected with the MSD and the TSQ are comparable, the
response times measured with the Balzers instrument are significantly
longer. This phenomenon is presumably due to poor sample gas
conductance through the 0.08-cm orifice in the Balzers gas-tight ion
source to which the 1/8-inch ME-MS interface tube is connected.

Table 5.5. The effects of analyzer conductance on response time.

response time (sec.)

 

anal er dichloromethane toluene
Finnigan 189-70 1 1 14
HP 5971-A MSD 10 1 1
Balzers QMG-5 1 l 20 3 5

MEMBRANE EXTRACTOR CONFIGURATION CONSIDERATIONS

In general, hollow fiber membranes provide greater extraction
efficiencies than do sheet membranes because of the greater sample
volume-to-membrane surface ratio and the higher sample linear
velocities obtainable. In addition, a flow-over hollow fiber membrane
probe can be inserted directly into samples, such as blood vessels in
the in vivo analysis of blood gases (29), that are beyond the reach of
sheet membranes. However, materials for sheet membranes are
commercially available in a wider variety of materials and dimensions.
In addition, without special equipment, custom-made membranes are

more easily prepared in sheet form than hollow fibers. Although the

140

majority of ME—MS work reported in the literature utilizes
poly(dimethylsiloxane) membranes, the development of practical
sample-membrane interaction models such as described in Chapters 3

and 4 will undoubtedly result in the use of a variety of materials.

Evaluation of flow-over and flow-through membrane extractors

The comparisons of absolute signal from the analysis of a sample
using a flow-over and a flow-through ME device shows a significant
advantage for the flow-through configuration. Approximately 50-fold
greater response was observed for the flow-through inlet as illustrated
in Figure 5.8. Collapsing of the soft membrane in the flow—over
configuration resulted in a significant reduction in effective membrane
area. Conversely, the inverted pressure drop in the flow-through
configuration takes maximum advantage of the membrane inner
radius/ thickness ratio. For identical volume flows, higher Reynolds
numbers are more easily achieved with the flow-through configuration.
However, there may be cases where the flow-over configuration is
preferred, as it can be made into a probe convenient for on-line

monitoring of hazardous or reactive chemicals (10, 16).

Neither the flow-through nor the flow-over inlet displays an
advantage in response time when similar sample flow conditions are
established. Under similar sample linear velocity conditions, the
enrichment factor is also independent of the configuration. The plot
in Figure 5.9 shows organic/water signal ratios for the flow-over inlet

vs. that for the flow-through inlet with comparable feed linear flows.

141

10000.00 -r

   
    
    

 

 

1000.00 --
8
‘5, flow-through
5
.r
§ 100.00 -
a
\
o
a
e
o
3' flow-over
c 10.00 -
a:
1.00 i i t i
0.01 0.1 1 10 100

Concentration Dichloromethane in Water, ppm

Figure 5.8. Comparison of response vs. concentration plots for the
flow-over and the flow-through membrane extractor configurations.

142

Response Ratio

Flow-over Organic/Water

 

 

 

0.0 l l .L 1. l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Flow-through Organic/Water Response Ratio

a = dichloromethane b = chloroform

c = bromodichloromethane d = dibromochloromethane
e = bromoform f = 1.1-dichloroethene

g = trichloroethene h = t trachloroethene

i = 1,1-dichloroethane j = 1,1,1-trichloroethane

k = toluene l = theylbenzene

m = chlorobenzene n =1,2-dichlorobenzene.

Figure 5.9. Relative organic [water response ratios for flow-over vs.
flow-through inlets obtained at comparable sample linear velocities.

143

As expected, no enrichment advantage is observed for either
configuration since the permeation rate for water also is affected by
the effective membrane area. Again, the flow-through configuration is
generally preferred because of the capability to more easily achieve
higher linear velocities at relatively low sample volume flows and the

effective membrane surface area is maximized.

Design of the ME Valve

An exploded view of the hollow fiber ME valve is shown in Figure
5.10. This ME device consists of two sections - upper and lower - of
the valve body, a valve plunger, a hollow fiber membrane, and some
sealant for attaching the membrane to the valve body. The lower
section of the valve body was fabricated to fit the upper section and
plunger from commercially available solenoid valves (1x259 24VDC
normally-closed solenoid valve from Kip Incorporated). The lower
section of the valve body is provided with two ports through which
samples are pumped into the valve body, through the hollow fiber
membrane, and out of the valve body. The membrane is a 2.5-cm
length of 0.0305-cm-i.d., 0.0635-cm.-o.d. Sflastic medical grade tubing
from Dow Corning Corp. The hollow fiber membrane is sealed into the
two sample port openings in the valve with Dow Corning RTV 734
Silastic sealant. The analytes selectively permeate through the
membrane and into the valve cavity. The permeate stream flows into

the mass spectrometer for analysis.

The sheet ME valve design in Figure 5.1 1 shows that the two

sample ports are connected internally by a groove. The membrane

144

O valve body:
if ‘upper section

#valve plunger

:5 U7 E 4—plunger seal

hollow fiber
membrane

 

 

 

 

 

 

 

 

sealant

 

    

 

 

\valve body:
lower section

sample ports

 

 

10 mass spectrometer

Figure 5. 10. Exploded view of the hollow fiber membrane extractor
valve.

145

valve body:

C:_5_>‘———--—*"““"”upper section

 

valve plunger

 

 

 

 

 

 

 

 

 

plunger seal

 

sheet membrane
support disc

    
 
  
  

4— sheet membrane

valve body:
lower section

 

 

 

 

‘sample groove

 

 

sample ports

10 mass spectrometer

Figure 5. l 1. Exploded view of the sheet membrane extractor valve.

146

lays across this groove, separating the sample from the valve cavity.
The preferred method for sealing the sheet membrane in the valve is
to 'sandwich' the membrane between the valve body and a donut-like
disc, as shown in Figure 5.11. A groove through the disc corresponds
to the sample channel in the valve body and provides a passage for
permeating materials to enter the valve cavity.

The ME valves were mounted to a probe and the ME-MS
interface was made with a 1/8-inch (0.32-cm) o.d., 0.22-cm-i.d.
stainless steel tube via the direct insertion probe inlet of the mass
spectrometer, as shown in Figure 5.12. In addition to the direct
insertion probe interface, the ME valve may be mounted directly to
the mass spectrometer in a manner similar to solenoid valves
commonly used for introducing calibration gases. The void volume in
the ME valves (~1 cm3) does not cause an excessive pressure surge in
the mass spectrometer when the valve was opened. Both the hollow

fiber and the sheet ME valves have been successfully evaluated.

No known ME device fulfills all of the requirements stated at the
beginning of this chapter for the ideal extraction/sampling device.
The advantages of the ME valve over some currently existing
technologr include a combination of the following attributes:

l) The temperature of the membrane and flow rate of the sample
may be well controlled with the ME valve.
2) The valve body provides protection to the membrane from

physical shock that may cause tearing or rupture.

147

 
  
     

   

permeate ‘ ‘_
flow s\\\x\\\\\\\\\\\r

  

 

   

“‘3‘2})}}7////////////////////////// .
\{{K((-’//////////////////////////

    

:
s
\\

   

         
     

direct insertion probe to interface tube

mass spectrometer

h

mass spectrometer
vacuum age
COHII'O er

 

 

 

power supply

 

 

 

Figure 5. 12. A membrane extraction valve coupled to a direct
insertion probe.

148

3) The solenoid may be powered through the vacuum-protection
circuit of the mass spectrometer so that in the event of a pressure
surge due to a membrane rupture or seal failure, the mass
spectrometer can be instantly isolated from the sample.

4) The device is constructed with a small void volume and surface
area. Response times and carry-over are minimized relative to those
of membrane extractor and valve in series. Although it may be
desirable to minimize the distance between the membrane extractor
and the mass spectrometer, this distance is not generally a transport-
rate limiting parameter. The interface tube can be made very short
and is typically heated independently of the ME valve.

5) The ME valve may be placed as close as possible to either the
process or the analyzer, depending upon the requirements of the
analysis. A variation of the ME valve described above may be used in
cases where it is desirable to contact the membrane directly with a
reactive or kinetic process. As shown in Figure 5.13, this variation
involves expanding the lower section of the valve body so that the
process actually occurs within the ME devices.

6) The ME valve may be useful in multiple stream sampling where
each sample stream requires a separate ME device. If the membranes
are housed inside of 3-way valves, then when one ME valve is not
activated, the valve cavity may be evacuated through the divert port to

an auxiliary vacuum pump to prevent accumulation of permeate.

149

 

  

Y\ .x\ .\.r..\.“ m
E -

m a m.“
2:.- -, m _ a.
......... r - § a

£4 a

W.- ///////////////

       

W543
k

of ME valve where the lower section of

the valve is expanded so that the process is carried out in direct

contact with the membrane.

Figure 5.13. A configuration

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(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

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Bredeweg. R A.; Langhorst, M. L.; Dittenhafer, D. R.; Strandjord,
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Tojo, K.; Ghannam, M.; Sun, Y.; Chien, Y. W. J. Cont. Release
1985. l. 197.

Petropoulos, J. H.; Tsimboukis, D. G. J. Membrane Sci. 1986.
27. 359.

Perry, R. H.; Green, D. Pem's Chemical Engineer's Handbook,
6th Ed.; Mcgraw-Hill Book Company: New York, NY; 1984.

Peters, T. L.; Stevens, T. S. U. S. Patent 4,684,470, 1987.

Stevens, T. S.; Jewett, G. L.; Bredeweg. R. A. Anal Chem 1982,
54. 1206.

152

(24)

(2 5)

(26)

(27)

(28)

(29)

Weast, R. C.; Astle, M. J .; Beyer, W. H.; eds. Handbook of
Chemisg and Physics,64th Ed.; CRC Press, Inc.: Baco Raton, FL;
1983; curve fitted from density data, p. F-5 and viscosity data, p.
F-38.

Crank. J. The Mathematics of Diffusion, 2nd Ed.; Oxford
University Press: New York, NY: 1971.

Korsmeyer, R. W.; Lustig, S. R.; Peppas, N. A. J. Polym Sci.
Polym Phys. Ed. 1986. 24. 395.

Everett, D. H. In The Solid-Gas Interface, Vol. 2, Flood, E. A., ed.;
Marcel Dekker, Inc.: New York, NY; 1967.

Lee, G. L.; Stern, S. A.; Mark, J. E.; Hoffman, E. Investigation of

Structure-Permeabiligg Relationships of Silicone Polmer
Membranes; Final Report October 1982 - September 1986; Gas

Research Institute: Chicago, IL.

Brodbelt, J. S.; Cooks, R. G.; Tou, J. C.; Kallos, G. J.; Dryzga, M. D.
AnaL Chem 1987. 59. 454.

153

CHAPTER 6

The Application of Membrane Extraction
Mass Spectrometry to the Analysis of
Gas and Liquid Process Streams

 

The efficiency of chemical processes is becoming an increasingly
important issue with the growing push toward waste reduction and
minimizing organic emissions in air and water. Analytical chemistry
can play a vital role in achieving and maintaining optimum process
operating conditions. As opposed to off-line analysis, on-line analysis
can provide more efficient use of information about a process in terms
of the amount of data, the quality of data, and the ability to respond to
changes in the process as exhibited by the data (1). As a simple
example, the continuos temperature measurements obtained with a
thermocouple device can provide a more statistically useful data set
and more precise indications of changes in the process temperature
than intermittent manual measurements with a thermometer. The
same is true for other traditionally measured process parameters such
as pressure and pH, as well as the more sophisticated measurements
of the process composition. Currently, on-line process composition
measurements are often obtained from chromatographic (2),
spectroscopic (3, 4), or solid state chemical sensor (5) techniques, as
dictated by the nature of the analyte and the process matrix. Although
the speed, sensitivity, and selectivity of mass spectrometry make the

154

technique attractive, on-line analysis by mass spectrometry has until

recently been limited to clean, well-defined gas phase streams.

Sampling is generally the most difficult problem associated with
the on-line analysis of process streams, regardless of the analytical
technique (6). Many gas and liquid process streams are chemically
and physically complex and require pretreatment prior to analysis.
This has been especially true for mass spectrometry, which has
generally utilized a capillary or orifice sample introduction system that
is limited to filtered gases. Many sampling problems can be
circumvented utilizing membrane extraction techniques. Advantages
of sampling with the silicone hollow fiber membranes include the
simplicity of the membrane extractor device, the high sample surface
area~to-volume ratio in the hollow fiber, the capability to obtain high
linear flows at relatively low volume flows, and the ability of the
membrane to provide efficient extractions of organic compounds from
both air and water. In addition, the inertness of the silicone
membrane material makes it suitable for use in many biological and
chemically reactive systems. The headspace gases in reactors have
been successfully monitored by ME-MS (7-10) as have liquid streams
(1 1-14). However, the simultaneous on-line analysis of the influent
and effluent gas and liquid streams of a reactor have not been

previously reported.

While previous work focused on the measurement of compounds
in either the effluent gas or the effluent liquid, all streams must be

considered for complete process characterization. Assumptions made

155

about the quantity of a compound in the influent stream can yield
significant errors in the mass balance determinations. As will be
demonstrated in this chapter, the measurement of the influent as well
as the effluent streams minimizes these errors. A generic process that
has liquid influent and effluent streams and gas influent and effluent
streams is illustrated in Figure 6.1. This chapter describes the
development of an on-line multi-gas /1iquid-stream monitoring
technique and its application to the simultaneous trace analysis of

complex and dirty streams in three wastewater treatment reactors.

EXPERIMENTAL SECTION

Chemicals

The compounds used in this study were obtained from Fisher
Scientific (Fair Lawn, New Jersey) and Aldrich Chemical Company
(Milwaukee, Wisconsin). These compounds were generally non polar
and relatively insoluble in water, so they were prepared in acetone to

facilitate dissolution when spiked into the influent wastewater stream.

Water standards were prepared in a l-L glass jar of deionized
water with the same solutions used to spike the influent water stream.
Air standards were prepared in a 100-L SaranTM (The Dow Chemical
Company, Midland, Michigan) bag filled with air by injecting known
volumes of 1:1 mixtures of the two compounds being studied. The

standards were analyzed following each reaction analysis.

156

membrane extractors

 

effluent
gas

 
    
 

   

effluent
liquid

 

    

 

PROCESS

R

influent
gas

influent
liquid

 

    

 

Figure 6.1. A configuration for the influent and efl'luent analysis by
ME-MS of a multi-stream, multi-phase process.

157

Analyzer

A Balzers QMG 51 1 quadrupole mass spectrometer was used in
this study. The mass spectrometer, sampling valve, and data
acquisition were controlled by in-house written software on a PDP 1 1-
73 computer from Digital Equipment Corporation (Maynard,
Massachusetts). The instrumental conditions were as follows:
Mass range: 60-200 daltons
Scan rate: 30 msec/dalton, 10 scans averaged
Secondary electron multiplier voltage: 1900 V for water streams, 2000
V for air streams.
Analyzer pressure: 1 X 10‘5 torr for water streams, 3 X 10'6 torr for
air streams.
The combination of 10 averaged relatively slow scans was selected
because these instrumental conditions provided very good sensitivity
for full scans in less than one minute. To the limit where ion
transmissions decay at high scan rates, the use of slow scan rates with
a quadrupole mass analyzer will provide signal-to-noise ratios
comparable to those obtained from averaging several fast scans over

the same duration of time.

Membrane and sampling system

The process streams were pumped from the reactors through
the membrane extractors via 6-meter long, l/8-inch (0.32-cm) o.d.
stainless steel tubes. The silicone hollow fiber membranes used in
this study were constructed by sealing 2.5-cm lengths of Dow Corning
(Midland, Michigan) SilasticTM medical grade tubing into 1/8-inch
stainless steel tubing tees, as shown in Figure 5.2. The two ends of

158

the hollow fiber membrane are sealed into stainless steel ferrules with
Dow Corning Silastic silicone sealant. For sampling the effluent air
streams, 0.0305—cm i.d., 0.0635-cm o.d. hollow fiber membranes were
used. The effluent air was pumped through the membrane extractors
at the rate of 60 cm3/ minute with an air pump from Metal Bellows
Corp. (Sharon, Massachusetts). Aqueous samples were drawn through
0.147-cm i.d., 0.196-cm o.d. hollow fiber membranes at the rate of 10
cm3 / minute with fluid pumps from Fluid Metering Corp. (Oyster Bay,
New York).

A 1 / 8 inch SC- 12-HT hastelloy-C rotary switching valve from
Valco Instruments Co., Inc. (Houston, Texas) was used to interface the
membranes to the mass spectrometer. This valve was computer-
actuated so that a different stream was sampled every 5 minutes. The
analyzer side of all inlets, when not selected for sampling to the mass
spectrometer, was continuously evacuated by a vacuum pump to
prevent accumulation of permeating species. The membranes and
valve assembly were mounted in an oven and maintained at 30 °C. The
permeation process is temperature dependent, as discussed in
Chapter 2, therefore the inlet was maintained slightly above the
process and maximum ambient temperatures. The analyzer vacuum
chamber and transfer line between the valve and the mass

spectrometer were heated to 100 °C.

Wastewater treatment apparatus
To demonstrate the utility of ME-MS for on-line reaction

monitoring of multiple streams, this study was performed with

159

Air-strip

0 .Str

 

 

 

 

 

 

 

 

 

 

 

 

  

Primam I ‘ eam
Stream
- - ~ - - Seconda
Stream
6 e
a e
a e
v _
TREATMENT
6
BASIN e 2 CLARIFIER
6' e
o e
-"

Air

Stream

Figure 6.2. A diagram of the wastewater treatment bioreactor.

bioreactors in a wastewater treatment pilot plant at the Dow Chemical
Company in Midland, Michigan. The pilot plant consists of three 75-L
reactors, depicted in Figure 6.2, that were designed to simulate a
large scale treatment process and were stocked with biomass from a
general wastewater treatment plant. The flow—through reactors were
composed of stirred treatment basins and clarifiers for recycling the
biomass back into the basins. The temperature of the reactors was

maintained at about 27 °C.

The influent wastewater was first filtered by IOO-um and 50-um
canister filters and then mixed with the spike solution in stirred l-L
glass mixing jars. A 10-cm3 syringe with a syringe pump from Sage
Instruments (Cambridge, Massachusetts) was used to inject the spike
solution at a rate of 5 pl / minute into the influent wastewater, which
was flowing into the mixing jar at a rate of 1 10 cm3/ minute (Figure
6.3). The caps of the mixing jars were fitted with TeflonTM-(E.I. du
Pont de Nemours and Company, Wilmington Delaware) coated silicone
rubber seals to prevent losses due to evaporation. The bioreactor
influent streams, flowing at a rate of 35 cm3 / minute, were drawn from
the wastewater stream flowing from the mixing jar. A second mixing
jar provided an unspiked wastewater stream to a bioreactor used to
generate baseline data. The wastewater flows were driven by
MasterflexTM peristaltic pumps from Cole Parmer Instrument
Company (Chicago, Illinois). The influent air continuously flowed at a
rate of 900 cm3/minute into the bottom of each basin. The tops of the
reactors were covered with polyethylene sheeting tight enough to

reduce the dilution of the effluent air stream due to air currents in the

161

Overflow
to Drain 25
cclmin.

    
 
 
 
     

to Basin 1
35 cclmin.

.—>
anary Stream
110 cclmin.

to Basin 2

to Sample 35 cclmin.

Inlet
10 cclmin.

SPIKED PRIMARY
STREAM MIXING
VESSEL

.................
..........

Overflow
to Drain 7O
cclmin.

 

Primary tream
110 cclmin.

to Basin 3
35 cclmin.

 

 

to Sample
Inlet
10 cc/min.

 

PRIMARY STREAM
MIXING VESSEL

 

 

 

 

Figure 6.3. The syringe and mixing jar configuration for spiking
organic compounds into liquid streams.

162

room, but not so tight as to cause a positive pressure in the reactor

headspace.

RESULTS AND DISCUSSION

The system developed has been tested and evaluated in the
context of process analysis. In many processes, both influent and
effluent streams need to be analyzed for complete characterization of
the process and to minimize errors due to impurities or inaccurate
assumptions about the influent composition. Results of the technology
development, performance tests, and an application of the technique

to real processes are described below.

Multi-gas/ liquid-stream analysis

By analyzing the streams influent and efiluent to a process, as
illustrated in Figure 6.1, mass balance determinations can be
performed and a more complete picture of a process can be obtained.
For a given component entering the process under non-reactive

conditions, the steady state mass balance equation is

mu + mig = mel + mgg (6.1)

and under reactive conditions is

mu + mtg = mel + meg + mp (6.2)

163

where m is the mass flow rate for the component in the stream
designated by the subscript, and where the subscripts i, e, l, and g
designate the influent, efiluent, liquid, and gas streams, respectively.

The mass flow rate due to uptake of the compound by the process is

designated mp. The values for mu, mtg, me], and meg are determined

from the on-line extraction and analysis of the streams and Hip is

calculated from Equation 6.2.

The mass flow rates for a component in the different process
streams are calculated by multiplying the process stream
concentration (mg/ L) by the process stream flow rate (L/ minute). For
example, the mass flow rate for a component in the influent liquid
stream is determined mass spectrometrically from the following

equation:

mm = Fu'Cfl = Fil.r'f'std,l.lil (6.3)

where C11 is the concentration of the component in the process
stream, Kstd is the analytical response factor for the compound
obtained from analyzing the liquid standards, and In is the response
for the compound in the process stream. This equation applies in the

determination of both liquid and gas phase mass flow rates after
substituting in the appropriate parameters.

It is useful to present the mass balance determinations in
Equations 6.1 and 6.2 as percent recovery or percent conversion,

defined as follows:

164

%Rec = 100%-(ma + meg)/(mfl + mig) (6.4)

%Con

100%-mp/(mfl + mig) = 100% — %Rec. (6.5)

Furthermore, the fate of unreacted materials in the process is
determined by calculating the percent recovery for the compound in
each effluent stream. For example, the unreacted percent recovery for

the compound in the liquid effluent stream is calculated as follows:

%Recel = 100%0mel/(mu + mig) (6.6)

The capacity to monitor multiple streams and even multiple
processes provides the ability to not only make mass balance
determinations, but also to analyze reference baseline streams (no
added reactants) to make these determinations more accurate. The
percent recovery for process A is obtained from Equation 6.7, where
the analytical results from process A are background corrected with

the results from the baseline process B.

%RecA = 100%0[(melA - melB) + (megA - megBH
/[(mflA - mflB) + (migA - migB)] (6.7)

More accurate results are obtained from determining percent
recoveries for each sampling cycle rather than calculating the
recoveries from time-weighted averages of each stream, since the
background levels and the baseline signals may not be constant over

time.

165

To demonstrate the utility of the ME-MS technique and the
importance of analyzing process influent streams, two aqueous streams
- one of which was continuously spiked with non polar organic
compounds - were analyzed. The streams were a complex matrix of
chemical wastewater containing solids and trace level organic
contaminants. The diagram in Figure 6.3 shows the syringe and
mixing jar configuration for spiking the aqueous stream with the
organic compounds. These compounds, their concentration in the
acetone dispersant, the mass/ charge ratios (m/z) of the ions used for
quantitation, and their mg/L-based response factors are listed in Table
6.1. Each spike set contained two of the compounds of interest. The
second wastewater stream, which was not spiked, was analyzed in the
same manner to obtain a baseline for calculating the spike
contribution. An advantage of using hollow fiber membranes for the
direct analysis of such complex samples is that fouling of the
membrane by solids is inhibited by the high linear sample flows which

continuously sweep the membrane surface.

Difficulty was encountered in spiking the aqueous stream - a
problem that underscores the importance of analyzing the process
influent streams. The measurements of some of the spiked
compounds in the stream exiting the mixing jar were initially as low as
5% of the calculated levels. The aromatic compounds in particular
showed very poor dissolution into the aqueous stream. Apparently, as
the spike solution approached the exit tip of the 1/16-inch stainless
steel syringe tubing, the acetone dissolved in the water stream, and

the more insoluble organic compounds either precipitated in the

166

Table 6. 1. Spike sets with volume % in acetone, monitored ions,
and standard response factors. Baseline response was 0.0005.

 

% in response/ mg/ L
spike sets acetone mlz in air in water
1 toluene 7.6 9 1 8.8 0.088

dichloromethane 5.0 84 0.6 0.0 16
2 benzene 7.5 78 9.0 0. 10
carbon tetrachloride 4.2 l 17 2.5 0.034
3 ethylbenzene 7.6 1 06 7.6 0.055
chloroform 4.4 83 2. 1 0.060
4 styrene 12.0 104 10.3 0.092
1 , 1 ,2-trichloroethane 7.6 97 2.5 0.030
5 chlorobenzene 6.0 1 1 2 1.4 0.018
tetrachloroethene 4.0 1 29 0.9 0.006
6 bromoform 3.8 173 0.8 0.007

1,1,1 ~trichloroethane 8.2 97 0.3 0.015

167

bottom of the Mg jar or dissolved back into the acetone solution in
the syringe. This problem was not observed when preparing
standards by quickly injecting 20 ul aliquots of the spike solutions into
a l-L jar of water. These results suggest that if the linear velocity of
the spike solution was increased sufficiently, more complete mixing of
the spiked organic liquids into the aqueous phase would occur. The
syringe was modified such that a 4-cm length of 50-um i.d. fused silica
tubing was sealed with epoxy into the tip of the syringe needle,
through which the spike solution flowed into the influent stream. The
modified syringe provided a calculated 400-fold increase in linear
velocity for the spiked solution and the spiking efficiency, for the most
part, improved dramatically.

The calculated concentrations based upon the amount of
compound spiked and the actual measured concentrations of the
compounds in the wastewater are listed in Table 6.2. In spite of the
improvements in the spiking technique, ethylbenzene continued to
exhibit poor spiking efficiencies, possibly due to a combination of the
low solubility for ethylbenzene in water (lowest among the compounds
studied) and the high affinity of ethylbenzene for solids as noted by
Hanna and co-workers (15). During the study of the wastewater
treatment process discussed below, the water exiting the mixing jars
was used as the liquid influent streams for the bioreactors. The
measured influent values - not the calculated values - were used in the
bioreactor mass balance determinations, thus minimizing the errors
that may result from the false assumption that the spikes were 100%
efficient.

168

Table 6.2. Spike concentrations (mg/ L) in the influent wastewater.

compound calculated measured
toluene 3.57 2.35
dichloromethane 3.57 3.40
ethylbenzene 3.47 0.49
chloroform 3.47 2.66
benzene 3.54 3.7 1
carbon tetrachloride 3.61 3.61
styrene 5.78 5.39
1, 1,2 trichloroethane 5.81 5.81
chlorobenzene 3.43 4.69
tetrachloroethene 3.36 3.75
bromoform 5.95 2.98
1 , 1 , 1 trichloroethane 5.95 3.78

Application to a biological wastewater treatment process

The analyses of volatile organic compounds in wastewater and air
are most commonly performed off-line after first extracting and
concentrating the organic compounds from the matrix (16, 17).
These procedures are often laborious, time-consuming, and require
sample manipulation. With ME-MS, the on-line extraction,
concentration, and analysis of the influent liquid and the effluent
liquid and gas streams from the process shown in Figure 6.2 were
performed nearly simultaneously. The influent air streams were
analyzed for purity by ME-MS prior to the on-line analyses, but were

not continuously monitored.

The process for the removal of volatile organic compounds from
the wastewater mainly occurs via two mechanisms in a bioreactor:

169

biodegradation and air-stripping. In many cases, these appear to be
rate-competitive processes such that biodegradation of many
compounds is improved when their residence time in the "biomass" is
increased, i.e., when air-stripping is reduced. However, for aerobic
biodegradation, aeration of the biomass is required, implying that
some air-stripping is inevitable. The process shown in Figure 6.2 was
studied by performing mass balance determinations for the organic
priority pollutants listed in Table 6.1. With the multi-gas/liquid-
stream analysis capability, process mass flow rates were determined
for three different reactors. As shown in Figure 6.4, each reactor was
prepared differently: In reactors 1 and 2, the influent wastewater was
continuously spiked to 3-6 mg/ L with the target compounds. Reactor
3, serving as the analytical blank or reference, was not spiked.
Reactor 2, the analytical test sample, was spiked, but its biomass was
rendered non-reactive by maintaining the contents at pH less than 2.

The aqueous streams were analyzed with the flow-through
silicone hollow fiber membrane extractor with a 0.147-cm i.d.. 0.196-
cm o.d. hollow fiber membrane. A Reynolds number value of
approximately 160 was achieved for the 10 cm3 / minute sample flows
from the wastewater influent and effluent streams. By minimizing the
effects of boundary layers, Reynolds numbers approaching 800 have
been shown to improve the membrane extraction efficiency for many
compounds as discussed in Chapter 5. Reynolds number values of 800
were achieved with a 10 cm3 / minute wastewater flow by utilizing a
0.0305 cm i.d. hollow fiber membrane, but plugging with solids and
sludge resulted. A sample flow of 50 cm3 / minute in the larger hollow

170

to vacuum

  
   

 

    

3

not
spiked

  
 
 

2
spiked

    
  
  

  

inactive active

  

iw = influent wastewater stream

iws = spiked influent wastewater stream
ia = influent air stream

ew = effluent water stream

ea = effluent air stream.

Figure 6.4. A process flow diagram illustrating the spiking and on-
line sampling of three wastewater treatment bioreactors.

171

fiber would be required to attain these Reynolds numbers, but due to
limits on sample consumption, 10 cm3/ minute was chosen as the
maximum flow rate. Zero sample consumption could have been
achieved by recycling the sample streams back into the process,
however, this was not done in this study. In any case, the sensitivities
were sufficient with the larger diameter membrane. The effluent air
samples were pumped through the 0.0305-cm i.d. hollow fiber at a
rate of 60 cm3 / minute. Convective mixing of the air streams is not as
important because the diffusion of organic vapors in air is much more

rapid than permeation through the membrane.

Mass flow rates were determined from the mass spectrometric
steady state process data and Equation 6.4. Pure air was used for the
influent gas, therefore mig = 0 for the organic compounds. Table 6.3
lists the steady state concentrations in mg/ L for the compounds in the
efiluent water and air streams in the reactive process (with the
background signal from reactor 3 subtracted). These data
demonstrate the capability of the technique to provide sensitive on-
line analyses of the physically and chemically complex multi-phase
process. Mass flow rate vs. time plots are displayed in Figures 6.5 and
6.6 for carbon tetrachloride and benzene, respectively, from the three
reactors. Carbon tetrachloride was observed to be much more inert to
the action of the biodegradation process than was benzene. as
discussed in more detail below. As demonstrated by these plots, mass
flow rate determinations can be more meaningful than concentration

values when defining a chemical process.

172

Table 6.3. Concentrations (mg/ L) detected in the eflluent water and
the air streams in the reactive process. Styrene and chlorobenzene
are not detected (N .D.) above the baseline in the eflluent water.

compound effluent water effluent air
dichloromethane 0.4 1 0.003
chloroform 0.32 0.044
carbon tetrachloride 0.07 0.046
1 , l , 1 trichloroethane 0.30 0.073
1 , l ,2 trichloroethane 2.09 0.076
tetrachloroethene 0. 1 5 0.065
bromoform l .58 0.026
benzene 0.07 0.005
toluene 0.31 0.012
ethylbenzene 0.0 1 0.005
styrene N.D. 0.003
chlorobenzene N.D. 0.003

The percent recoveries for reactor 1 were calculated from
Equation 6.7 with reactor 3 providing the background values. The
percent recoveries from reactor 2 were calculated from the steady
state mass flow rates using Equation 6.4. A fourth reactor, not spiked
and containing non-reactive biomass, would provide baseline data for
reactor 2, but was not available for this study. For these calculations, it
was assumed that the signal was due entirely to the compound of
interest. The percent recoveries for each compound in reactors l and
2 are summarized in Table 6.4. Had the amount of spiked compound
added to the reactor influent been assumed to be correct and not
measured, serious errors in the mass balance determinations would

have resulted. The data in Table 6.4 demonstrate the capacity of the

173

 

0.10 'P

0.08 '-

0.06 r-

.o
2
§

0.02 ..

 

 

 

0.12 -

Mass Flow Rate, mg/mln.

0.10 .

0.08 I

0.06 '

0.04 -

0.02 1

 

 

 

 

 

0.0 10.0 20.0 30.0 40.0

Time, hours

iw = influent wastewater stream
ew = the efiluent water stream,
ea = efiluent air stream

Figure 6.5. Mass flow rate plots for carbon tetrachloride in A, reactor
3 (reactive, not spiked), B, reactor 2 (non-reactive, spiked), and C,
reactor 1 (reactive, spiked). The spike was begun at the 8-hour mark.

174

0.04 «-

 

 

 

.0

 

 

 

 

 

O

O
N

A
0.02 «-
v I'w‘ew
o . . . ’d—l

0.12 ~-
. B iw
r:
E 0.10 "'
\
or
E 0.08 ..
o“
g 0.06
I
3 0.04
2
IL
in
a
a
2

0.12

 

 

 

 

0.10 ~-
0.08 ..
0.06 4-
0.04 --
0.02 -- I
a
0' fl i A La“
0.0 10.0 20.0 30.0 40.0
Time, hours

Fey:
IW = influent wastewater stream
ew = the effluent water stream,

ea = effluent air stream

Figure 6.6. Mass flow rate plots for benzene in A, reactor 3 (reactive,
not spiked), B, reactor 2 (non-reactive, spiked), and C, reactor 1
(reactive, spiked). The spike was begun at the 8-hour mark.

175

on-line analytical system to determine the relative inertness of
different organic materials to a reactive process, where the substances

exhibiting higher percent recoveries are more inert to the process.

Table 6.4. Percent recoveries and standard deviations for the
spiked organic compounds.

compound reactive process non—reactive process
dichloromethane 15; 1 100; 4
chloroform 64; 3 92; 5
carbon tetrachloride 42; 1 72; 3
1,1,1 trichloroethane 69:4 85; 6
1,1,2 trichloroethane 77; 7 87; 8
tetrachloroethene 59; 7 103; 4
bromoform 80; 14 105; 12
benzene 6; 4 88; 4
toluene 29; 2 100; 6
ethylbenzene 34; 33 l 13; 20
styrene 2; l 75; 6
chlorobenzene 2; 1 96; 3

The capacity to determine the relative air-stripping process
efficiencies for the different compounds is also demonstrated. The
fractions of the organic compounds remaining in the effluent water
and removed from the water by the air—stripping process were
calculated using Equation 6.6 and are given in Tables 6.5 and 6.6,

respectively. Again, the results for reactor 1 are baseline-corrected.

176

Table 6.5. Percent recoveries and standard deviations in the

eflluent water streams.

compound
dichloromethane

chloroform

carbon tetrachloride
1,1,1 trichloroethane
1,1,2 trichloroethane
tetrachloroethene
bromoform

benzene

toluene
ethylbenzene

styrene

chlorobenzene

reactive process
12; 1
12; 2
2; 1
8; 2
36; 4
4; l
53; 11
2; l
13; 1
1; 1
0; l
0; 1

non-reactive process
30; 2
18; 1
11; 1
10; 1
41; 4
9; l
74; 1 1
24; 1
21; 2
19; l
18; 1
17; 1

Table 6.6. Percent recoveries and standard deviations in the

eflluent air streams.

compound
dichloromethane

chloroform

carbon tetrachloride
1,1,1 trichloroethane
1,1,2 trichloroethane
tetrachloroethene
bromoform

benzene

toluene
ethylbenzene
styrene
chlorobenzene

reactive process

3; 1
52;3
40; l
6l;4
41:3
55;7
27;3

4;3
16; l
33;33

2; 1

2; l

177

non-reactive process

70; 2
75; 4
61; 3
75; 5
46; 4
94; 4
31; 3
64; 2
79; 5
94; 20
58; 5
79; 3

The background-corrected fraction of organic material removed
due to uptake by the biomass in reactor 1 was calculated from
Equation 6.5. This bio-uptake term represents the unrecovered
fraction of material and may be a combination of biological
fermentation and absorption. The actual percent removal due to the
biomass may be affected by other factors. Deviations from 100%
recoveries in the non-reactive process in reactor 2 are presumed to be
due to experimental error as well as the presence of solids. These
deviations are assumed to be consistent for the three reactors.
Therefore, given the capacity to monitor all of the reactors, the
recoveries from reactor 2 could be used as correction factors in

calculating corrected bio-uptake values:

%Bio-uptakeflcorrected) = 100%-[1 - (%Rec1/%Rec2)] (6.8)

Both the uncorrected and corrected (given in parentheses)
values for the bio-uptake are listed in Table 6.7, along with values
reported in the literature from off-line analyses (18-23). The
capability to demonstrate the relative reactivity of the different
compounds in biological wastewater treatment processes is provided

by these analyses.

In most cases, the percent bio-uptake results from this study are
consistent with the percent biodegradation values reported in the
literature. The greatest disparity is observed for 1,1,1-trichloroethane
and tetrachloroethene, where essentially no biodegradation was

reported in one literature reference (18), although bio-uptake of 19%

178

Table 6.7. Percent bio-uptake and standard deviations.
Experimental values corrected for the recoveries in the analytical
test reactor (reactor 2) are given in parentheses.

compound

dichloromethane
chloroform

carbon tetrachloride
1,1,1 trichloroethane
1,1,2 trichloroethane
tetrachloroethene
bromoform

benzene

toluene
ethylbenzene

styrene

chlorobenzene

a = Reference 18
b = Reference 19
c = Reference 20
d = Reference 21
e = Reference 22
f = Reference 23.

 

experimental literature
85; l (85; 1) 50-95b, 100d, 966
37; 3 (31; 4) 50-95b, 0a
58; 1 (41; 4) 50-95b
31;4 (19; 4) 513.03
23; 7 (12; 2)
41; 7 (42; 7) 03
20; 14 (24; 7)
94:4 (94; 4) 50-95b, 85-88f
71;2 (71; 1) 50-95b, 84-88f, 40-79C
66; 33 (70; 28) 50-95b, 85-97‘.
98; 1 (97; 1)
98;1 (98;1) 913, 79-93C

179

and 42%, respectively, were observed in this study. As with any
process, biodegradation is highly dependent upon the reaction
conditions. The age and species of biomass, organic influent
concentration, mineral nutrient content, process flow rate (retention
time), oxygen concentration, temperature, pH, and other factors
influence the biodegradation process. As is apparent from the
comparison of literature values, the results can vary widely depending
upon these process conditions. For example, one study (18) showed
no biodegradation of chloroform (as well as 1,1,1-trichloroethene and
tetrachloroethene), while another (19) reported the biodegradation of
chloroform to be in a range of 50-95%. A corrected value of 31% bio-

uptake for chloroform was observed in this study.

In spite of the use of filters, the flow of sludges and small
particulates was constantly observed in the influent wastewater. The
concentration of solids was not constant and could not be predicted.
The influent water was sometimes clear one day and turbid with solids
the next day. These solids apparently were road dirt (earth moving
vehicles were working in the area), tars, and sludge from aggregated
biomass. Extracting the organic compounds from this physically
complex wastewater matrix was a crucial step in these experiments,
because sample matrix effects can lead to large errors in trace analyses
(24). Even small errors in a stream analysis may result in large errors

in the mass balance determinations.

Frequently, the presence of solids affected the process when the
solid levels became particularly high in the influent wastewater,

180

causing the recoveries to become significantly depressed. For
example, when high turbidity was observed during one process
analysis, mass balance determinations for dichloromethane and
toluene around the non-reactive process (reactor 2) showed
recoveries of only 39% and 32%, respectively. Large differences were
still observed between the reactive and non-reactive processes for this
experiment, where mass balance determinations around the reactive
process (reactor 1) showed recoveries of only 1.6% for

dichloromethane and 1.0% for toluene.

These results demonstrate the capacity of the analytical system
to monitor the effects of solids on the emissions of organic vapors
from wastewater. However, the absorption of the organic compounds
into the solids represented another process, thus introducing another
uptake variable into the mass balance equation. This second uptake
variable was difficult to separate from the bio-uptake variable and it
was not within the scope of this study to do so. Therefore, when poor
recoveries were observed from reactor 2, the experiment was
repeated after the influent water became less turbid. As a result, the
recoveries were sufficient for reactor 2 (mean percent recovery = 93,
o = 12) considering the complexity and the concentration levels of the
process streams. Relatively large standard deviations in the recoveries
exhibited for ethylbenzene are likely due to its low influent
concentration (0.49 mg/ L) which enhances the effects of random
error and process baseline changes. Again, these results demonstrate
the importance of analyzing the influent stream rather than relying on

the calculated spike values.

181

When the process flows were interrupted for some reason (e.g.,
pump failure or plugging of the stainless steel sampling tubes) and
solids dried on the membranes, the permeation characteristics
changed. This happened occasionally and simply required
replacement of the membranes. Following each study (every 3-4
days), the sample tubes and membranes for sampling the wastewater
streams were flushed with clean tap water and allowed to sit for
several hours to prevent the growth of anaerobic bacteria on the inside
of the tubing. The membranes that were used to sample the gas
streams showed no observable change in properties throughout these

experiments.

CONCLUSIONS

It has been demonstrated that, with little or no sample
preparation, membranes can be used as an effective interface between
complex and dirty matrices (gas and liquid) and a mass spectrometer.
The use of a single technique and a single analyzer for a multi-phase
and multi-stream process minimizes experimental errors and
simplifies calibration. The analytical system can be used to study,
optimize, and potentially to help control and automate processes. In
addition to the determination of the fate of organic compounds in
waste treatment processes, other applications include the on-line
study of fermentation, distillation, absorption, devolatilization,
stripping, degassing, and membrane separation processes. The
reliability of the continuous analysis of such processes depends upon a)

the general reliability of the analyzer, b) the reliability of the sampling

182

system, and c) the reliability of the process itself. Mass spectrometers
for process monitoring are commercially available and have
demonstrated reliability for specific applications. However, as stated
at the beginning of this chapter, sampling the process is generally the
limiting factor such that the analyzer is only as good as the sample
introduction system. Ultimately, the analysis depends upon routine
maintenance and the continuous operation of the process at the range

of conditions for which it - and the sampling system - was designed.

183

REFERENCES

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Callis, J. B.; Illman, D. L.; Kowalski, B. R. AnaL Chem. 1987, 59,
624A.

Manka, D .P. Automated Stream Analysis for Process Control,
Vol. 1; Academic Press: New York, NY; 1982.

Eckstein, R. J.; Owens, G. D.; Baim, M. A.; Hudson, D. A. Anal.
Chem. 1986, 58, 2316.

Seitz, W. R. Anal. Chem 1984, 56, 16A.

Schuetzle, D.; Hammerle, R. Fundamentals and Applications
of Chemical Sensors, ACS Symposium Series 309; American
Chemical Society: Washington, DC; 1986.

Blaser, W. W.; Ruhl, H. D.; Bredeweg. R. A. Amer. Lab. January
1989, 69.

Tou, J. C.; Westover, L. B. J. Phys. Chem. 1974, 78, 1096.

Kallos, G. J.; Tou, J. C. Environ. Sci. TechnoL 1977, 11, 1101.

Savickas, P. J .; LaPack, M. A.; Tou, J. C. Anal. Chem 1989, 61,
2332.

Van Nugteren-Osinga, I. C.; Bos, M.; Van Der Linden, W. E. Anal.
Chim. Acta 1989, 226. 171.

Pungor Jr,. E.; Pecs, M.; Szigeti, L.; Nyeste, L. AnaL Chim. Acta
1984. 163, 185.

Heinzle, E.: Reuss, M. Mass Spectrometgz in

Biotechnological Process Analysis and Control; Plenum Press:
New York, NY; 1987.

184

(13)

(l4)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

Bier, M. E.; Kotiaho, T.; Cooks, R. G. Anal. Chim. Acta 1990,
231, 175.

Hayward, M. J.; Kotiaho, T.; Lister, A. K.; Cooks, R. G.; Austin, G.
D.; Narayan, R.; Tsao, G. T. Anal. Chem 1990, 62, 1798.

Hanna, S. A.; Austem, B. M.; Eralp, A. E.; Wise, R. H. J. Water
Pollut. Control Fed. 1986, 58, 27.

EPA Test Methods for Evaluating Solid Waste, Volume 1B;
Methods 8240 and 8270; U.S. EPA Office of Solid Waste and
Emergency Response: Washington, D.C.; 1986.

NIOSH Mannual of Analytical Methods, 3rd Ed.; Methods 1003
and 1501; P. M. Eller, ed.: U.S. DHHS (NIOSH) Publication No.
84-100; U.S. Government Printing Office: Washington DC.

Bouwer, E. J .; McCarty, P. L. Environ. Sci. Technol. 1982, 16,
836.

Eckenfelder Jr., W. W.; Patoczka, J .; Watkin, A. T. Chem Eng.
1985, 60.

Kirsch, E. J .; Wukasch, R. F. Report to Municipal Environmental
Research Laboratory; Office of Research and Development, U.S.
Environmental Protection Agency: Cincinnati, Ohio, 45268.

Klecka, G. M. App. and Environ. Microbiology 1982, 44, 701.

Rittrnann, B. E.; McCarty, P. L. App. and Environ. Microbiology
1980. 39, 1225.

Kincannon, D. F.; Fazel, A. 4lst Annual Purdue Industrial Waste
Conference, Purdue University, West Lafayette, Indiana, 1986.

U.S. EPA Method 1624 and 1625; Federal Registry, 49(209);
1984.

185

APPENDIX

Permeation Measurements

 

The direct measurement of permeation parameters is commonly
made by exposing the feed side of the membrane to a pure substance
at a known pressure while measuring either the increasing pressure at
the permeate side of the membrane with a pressure gauge (1) or the
permeate flow with a flow meter (2, 3) or a simple detector such as a
thermal conductivity detector (4, 5). Other methods include
measuring the weight gain of the polymer in the presence of the gas of
interest (6, 7). These techniques only allow for the analysis of a single
component at any time and may suffer from interferences if the
substance being tested is not pure or if the chamber leaks on either
side of the membrane. In addition, contacting silicone with most pure
organic solvents results in swelling of the polymer, yielding non-
Fickian behavior. The sensitivity and specificity of a mass
spectrometer provides for permeation rate measurements at low

concentrations and independent of other components (8-10).

The response of the mass spectrometer to a gaseous substance
flowing into the ion source, either by permeation through a membrane

or by effusion through an orifice, is ideally given by Equation 2.8. The

mass spectral response factor, 91, is not easily measured with a
membrane, but may be obtained by analyzing gas standards from a

186

large reservoir through an orifice in a thin metal foil (1 1). At
sufiiciently low pressures or small orifice size (i.e., orifice radius

smaller than the mean free path for gases), the flow rate of a

component through an orifice of area A0 into a vacuum is given by (12)

F1: 0.225-A00pi/(M10R'DI/2 (A. 1)

where p1 is the partial pressure of component i in the reservoir, M1 is

the molecular weight of the component, R is the ideal gas constant,

and T is the absolute temperature. Therefore,

Q: = 11 (M10 )1/2/(0-225'Ao'p1) (A.2)

where Ii is the analytical response for the component. With the
determination of 9,, the permeability may be determined by

substituting Equation 2.8 into Equation 2.6 or Equation 2.7. For the

sheet membrane,

P1 = DI,S.Kl = (rf10d)/(QpA) (A.3)

The value for D51 is determined from the permeation response curve

and Equation 2.13, and K1 is calculated from the ratio

K1 = Pl/D1,S (A.4)

The components of the permeation response curve used to determine

P1 and DLS are shown in Figure A. 1.

187

 

 

P = rf-d/(QA) = Ds-K

 

    

ANALYTICAL RESPONSE

Ds = 0.14’d2/t(5o)

 

 

 

 

to 1(50) TIME

Figure A. 1. hperimental determination of permeation parameters.

188

It is generally true that any quantitative analysis (i.e., the
permeation rate measurement) should be performed soon before or
after standardization of the analyzer (i.e., by the orifice technique).

The number of compounds that can be studied in a reasonable time
period is limited by the operations such as switching back and forth
between the orifice and the membrane extractor. In addition, the
permeation measurements may be time-consuming for larger organic
molecules since they require not only the time to reach steady state
permeation following a step change in the sample concentration, but
time is also required to achieve a baseline following removal of the
sample and prior to the next sample introduction. A more efficient
approach to these measurements is to determine values for 91 for the
compounds to be studied and normalize all of them to one of the
compounds. These response factors, many of them relative to toluene,
have been previously determined by a method developed by Caldecourt
(1 l) for a large number of compounds and tabulated in a Dow Chemical
Analytical Sciences mass spectral data base (13). A similar data base,
with response factors relative to butane, has been generated by the
Shell Oil Company (14). The relative response factor is defined here

as follows:

C11 = (It/Wt1/(Il/Wx) (A.5)

where w is the weight of the substance injected into the reservoir and

the subscript t indicates toluene, which is chosen to be the compound

to which all others are normalized. Values for qj for several

compounds examined in this work are listed in Table A.1. For a given

189

Table A. 1. Mass spectrometric response factors, relative to toluene,
used to determine permeation parameters.

compound ml; relative response factor
nitrogen 28 0.39
oxygen 32 0. 5 1
argon 40 0.33
carbon dioxide 44 0.49
methane 1 6 0.27
ethene 27 0. 7 1
ethane 30 1 .2 1
propane 44 l .96
butane 58 4.03
pentane 43 1 .75
hexane 43 1 .70
heptane 43 1.09
benzene 78 0.65
toluene 92 1 .00
ethylbenzene 1 06 1.93
chlorobenzene l 1 2 1.07
chloromethane 50 0.82
dichloromethane 49 l .4 1
carbon tetrachloride l 1 7 3.90
chloroethene 62 l . 10
1 , l -dichloroethene 6 1 1.87
trichloroethene 95 2.8 1
tetrachloroethene 94 1 1.3
bromomethane 94 2. l 8
dibromomethane 93 3. l 5
bromoform 9 1 20.8
water 1 8 0.96
methanol 3 l l .03
ethanol 3 l 1.29
1 ~propanol 3 1 0.67
2-propanol 45 0.74
1 -butanol 56 1 .53
acetone 43 0.93
2-butanone 43 0. 73

190

mass spectrometer under proper operating conditions, the relative
response factor is a constant. Day-to-day instrument drift resulting in
variations in the response for one substance will result in proportional
variations in response for the second substance. When a different
mass spectrometer is used, additional errors are introduced.
However, with proper tuning of the analyzer, these errors are
minimized and the permeation parameters may be adequately
estimated for several compounds in a relatively short period of time.

The weight of the standard added to the reservoir is related to
the partial pressure by the ideal gas equation, where w, =

pIOMIOV/(R-T), which when substituted into Equation A.5 yields the

following:

‘11 = [at/Pt)/(11/P1)1'1M1/Mt1 (A.6)

The relationship between this relative response factor and the

absolute response factor in Equation A.2 is given by

Qt/Qi = C11‘1Mt/ M113/ 2 (A.7)

Applying Equation A.3 to this relationship yields the enrichment factor

for compound 1 relative to toluene

Ei/t = Pl/Pt = q1°(rfi/rft)0(Mt/M1)3/2 (A.8)

191

If Pt is measured by the technique described above, then the

permeabilities for all of the components where ql values are available

can be easily estimated.

As stated previously, most of the permeation parameters for
gases such as nitrogen are known for many membranes. It can easily
be shown that the enrichment factors relative to nitrogen for the

components where qi is known can be determined by the following

equation:

31/N2 = Pi/PNZ = (Ffi/l'sz)'(Ch/CIN2)'(MNz/M113/2 (A9)

The advantages to using this solution are 1) as stated above, the
permeability parameters for nitrogen are well established for most
membrane materials and 2) the nitrogen matrix, in which most
standards are prepared, is much more representative of the air matrix
most commonly encountered in true analytical applications. A similar
equation is used to determine the enrichment factors relative to

water.

ERROR ANALYSIS

Assuming that errors in the calculated permeation parameters
are random, and that the sources of these errors can be identified and
their magnitudes estimated, then the relative standard deviation for
each parameter can be estimated. The relative variance for a

measurement is given by the square of the relative standard deviation.

192

The relative standard deviation for the calculated permeation
parameters is given by the square root of the sum of the variances for
all of the sources of error (15). The equations used to calculate the
permeation parameters and their corresponding relative standard

deviation expressions are summarized as follows:

Enrichment factor (relative to nitrogen)
8r/Nz = (11/ 1N2)°(cN2/ c1)'(q1/ qN2)'(MN2/ M1)3/ 2 (A. 1 0)

Baum/81mg = Kali/lip + (BIN2/1N2)2 + (Sci/Ci)2
+ (acj/ci)2 + (aq1/q1)2 + (£)qj/qj)2}1/2 (A.1 l)

The relative response factors, qi and qu, are assumed to be

consistent from one mass spectrometer to another, as stated above.

The molecular weights, M, and MN2’ used in Equation A.10 are

assumed to be accurate.

Permeability
Pi = PN2.81/N2 (A. 1 2)
aPi/Pi = [PNz/Pd'aei/NZ = aei/Nz/el/Nz (A. 1 3)

The value for the permeability of nitrogen, PN2’ used in Equation A. 12

is assumed to be accurate.

193

Diffiisivity

1),,S = 0.14-d2/(t50-t0) (A. 14)

aDm/DLS = (wad/(1)2 + ([at50-3t01 /[t50-t0])2}1/2 (A. 15)

The error in the response time measurement is dependent upon

the error in determining the time of initial contact of sample with the
membrane, to, and in determining the time where one-half steady

state permeation is achieved, t5o, as described in Chapter 2. The

error in the time of initial contact is estimated to be approximately

;0.5 seconds. The error in the measurement of the time required for

one-half steady state permeation is the difference in times between
data points (;O.25 seconds) in the ion intensity vs. time permeation

profile plot.

Distribution ratio

Ki = 76 CHIHg'Pi/DLS (A. 16)

3K1/ K: = {(3P1/ P02 + (8D1,s/D(,s)2}1/2
= {(aei/Nz/ 81/N2)2 + (3D1,s/ Di,s)2}1/ 2 (A. 17)

The total sample pressure, pt = 76 cmHg, used in Equation A. 16

is assumed to be accurate.

194

Values estimated for the relative standard deviation for each
known source of error are given, along with the relative standard
deviations for the computed results for enrichment factors,

permeabilities, diffusivities, and distribution ratios, in Table A.2. The
relative standard deviations estimated for the analytical signals, 11, and

the response times, (t50-t0), are compound-dependent. Compounds

that demonstrate poor analytical sensitivities and short response times
exhibit the greatest relative variances. However, these sources of
error are typically negligible when compared with the errors
estimated for the relative response factors, qi, and the membrane
thickness, d. The range of the relative standard deviations for the
analytical responses does not affect the error analysis for the
enrichment factors or the permeabilities. The range of the relative
standard deviations for the response times only slightly affect the
error analysis for the diffusivities and the distribution ratios. The
tolerance reported for the membrane wall thickness (16), Bd/d =
31%, is much larger than observed experimentally. In the current
studies, relative standard deviation for the membrane thickness is
more reasonably estimated to be less than 10%, in which case the
range for the relative standard deviation for diffusivities is 20-24% and
for the distribution ratios is 24-28%.

195

Table A.2. Relative standard deviation for each known source of
error and for each computed permeation parameter.

known source of error

311 /11

aINz/INz

aq/ c1

ach/CNZ

3(11/ C11

a<1N2/ C1N2

ad/d

(3t50'3t01/ “so-to)

r_e_$_u_|1
881/N2/31/N2
ar>,/r>l
8D1,s/ Di,s
arc/Ki

range of estimated
relative standard deviation

2.9X10'2-1.7 %
6.0X10'3 %

1.0 %

1.0 %

10 %

10 %

31 %

0.21-14 %

14 %
l4 %
62-64 %
64-66 %

196

REFERENCES

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Barrer, R. M. Trans. Faraday Soc. 1939, 35, 628.

Brubaker, D. W.; Kammermeyer, K. Ind. Eng. Chem 1952, 44,
1465.

Stancell, A. F. In Polmer Science and Materials, Tobosky, A. V.;
Mark,H. F., Eds; Wiley-Interscience: New York, NY, 1971.

Pasternak, R. A.; Schirnscheirner, J. F.; Heller, J. J. Polym Sci.
1970. 8. 467.

Ziegel, K. D.; Frensdorff, H. K.; Blair, D. E. J. Polym Sci. 1969, 7,
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Laatikainen, M.; Lindstrom, M. J. Membrane Sci. 1986, 29, 127.

Ho, J. S.-Y.; Schlecht, P. C. Am Ind. Hyg. Assoc. J. 1981, 42, 70.

Eustache, H.; Histi, G. J. Polymer Sci. 1981, 8, 105

Harland, B. J .; Nicholson, J. D.; Gillings, E. WatRes. 1987, 21,
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(10) Ton, J. C.; Rulf, D. C.; DeLassus, P. T. AnaL Chem 1990, 62, 592.

(l 1) Caldecourt, V. Anal. Chem 1955, 27, 1670.

(12) Barrow, G. M. Physical Chemism, 4th Ed.; McGraw-Hill: New

York, NY; 1979.

(1 3) Analytical Sciences Mass Spectral Data Base, internal

communication, The Dow Chemical Co., Midland, MI.

197

(14) Caldecourt, V., personal communication.

(15) Laitinen, H. A.; Harris, W. E. Chemical Analysis, 2nd Ed.; McGraw
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(16) Medical Materials Business Product Form No. 51-769A; Dow
Corning Corp., Midland, MI.

 

198

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