A study of organic compound pervaporation through silicone rubber

Journal of Membrane Science, 49 (1990) 171-205 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

A STUDY OF ORGANIC COMPOUND THROUGH SILICONE RUBBER

171

PERVAPORATION

J.M. WATSON* and P.A. PAYNE Department of Instrumentation and Analytical Science, Uniuersity of Manchester Institute of Science and Technology, P.O. Box 88, Manchester M60 1QD (Great Britain) (Received March 10,1989; accepted in revised form July 25,1989)

Summary Through a process of selected experiments, literature reviews and simple assumptions in which such phenomena as concentration dependent diffusion, coupling effects and swelling effects are ignored, we have attempted to produce a simple though comprehensive framework of understanding of the pervaporation of dilute organic compounds through silicone rubber. In this way, we have derived a simple and useful relationship between pervaporate composition and downstream pressure; offer a quantitative interpretation of the relationship between separation factor and solution concentration; illustrate the greater importance of the solubility over that of the diffusion coefficient as regards separation; and indicate the influence of the permeant organic functional group on the diffusion coefficient. Such a comprehensive picture, we believe, is a useful contribution to the understanding of the pervaporation process in silicone rubber.

Introduction Some time ago, prompted and supported by two commercial companies, we began an investigation into the use of membranes for the purpose of sampling from liquid streams by the pervaporation process. The vapours so produced are normally subjected to chemical analysis and in this way the liquid composition is continuously monitored and in some cases subsequently controlled. While the technique is not new [ 1 ] it is apparent that it has two major problem areas, namely, the lack of a clear understanding of the pervaporation process itself, and the problems arising from the very wide range of organic structures and functional groups likely to be encountered in real sampling and analysis situations. The total investigation is therefore quite a demanding one, and only the former problem is dealt with in this paper; we may now be in a better position to tackle the latter one. Although such a membrane application is largely overshadowed by the potentialities of pervaporation membranes for the large-scale separation of liquid *To whom correspondence should be addressed.

0376-7388/90/$03.50

0 1990 Elsevier Science Publishers B.V.

172

mixtures, the underlying science is nevertheless clearly the same. To understand the sampling process therefore, it is desirable to develop a quantitative appreciation of the processes underlying the pervaporation process itself, namely, the solubility of the permeant in the membrane, the diffusion of the permeant through the membrane, and the evaporation of the permeant from the membrane at the downstream face. To this end, and throughout the course of this work, considerable attempts were made to utilise the relevant membrane literature, with the aim of establishing what was already known, both to help identify key areas for experimental investigation, and to compare our own results. Mastering membrane literature is not an easy task. For a start, in spite of its vast volume, very little of the knowledge gained seems to have filtered down to standard physical chemistry texts, possibly explaining a perceived lack of general knowledge concerning membrane function. More significantly perhaps, no review of the pervaporation process of which we are aware, appears to convincingly establish the sort of simple quantitative framework of understanding that is often useful, either as an overview, or as a starting point for subsequent investigations into the many complicating features that are known to frequently occur. For example, although the dependence of the pervaporate composition on the downstream pressure is an important consideration in macro-separation processes, as it is in sampling and analytical applications, a review of the basic principles of pervaporation by Aptel and Neel [ 21 offers no explanation of this dependence, and very little discussion. A review by Neel et al. [3] provides considerably more discussion but is largely concerned with aspects of a particular case. On the other hand, extracting a simple quantitative description of the phenomenon from the very comprehensive work of Shelden and Thompson [4], or of Brun et al. [5], for example, is a rather laborious task. In view of the above considerations, together with other matters concerning permeant solubility and diffusion, we eventually set out to establish our own broad framework of understanding of the pervaporation process as it occurs in silicone rubber, through the use of simple arithmetic involving simple and familiar concepts, simple and rapid experiments, and critical literature reviews. We believe that such a framework is not only useful in itself, but is also a useful aid to the understanding of the more complex processes. What follows is a concise account of that work; we believe that such an account does not exist elsewhere in the membrane literature. Although in this paper we do not lose sight of our interest in sampling and analysis, our results and comments may possibly be of interest to a wider readership. In these investigations a dimethyl silicone rubber membrane (supplied by ESCO (Rubber) Ltd. ) was used because of its high permeability [ 61. During the course of this work we became aware of the new and more permeable polymer [ 71, poly [ l-trimethylsilyl-1 propyne] (PTMSP), which could have a sig-

173

nificant role in sampling and analysis situations. All liquids used in this study were binary aqueous organic solutions and the pervaporate vapour analysis was achieved using a mass spectrometer. Further experimental details are given in Appendix I. The permeation

equation

According to the solubility-diffusion-evaporation model, the membrane permeation flux, J, from liquid to vapour phase is given by [ 81: J=DCm(l-p/@)/Z

(1)

where D is the diffusion coefficient, c” is the concentration in the membrane at the liquid/membrane interface, p is the actual vapour pressure maintained at the vapour/membrane interface andp” is the vapour pressure in equilibrium with the liquid at the liquid/membrane interface, all quantities corresponding to a single species present in the liquid; 1 is the membrane thickness. This equation must be thought of as an approximate membrane equation since it is based on assumptions [8] whose validity may have to be questioned in the light of experience; nevertheless we now proceed to explore its implications. The vapour

composition

Suppose that the liquid is a binary solution with components denoted by subscripts o and w, and that their vapours exist at the vapour/membrane interface in the steady-state partial-pressure ratio, p,/p,. That this ratio is dependent on the downstream vapour pressure is well known and the basic explanation of this dependence is self-evident; if the downstream pressure is maintained at a sufficiently low value by continuous vapour removal, then the resulting vapour composition will be determined solely by the vapour fluxes issuing from the membrane and hence will be membrane-dependent; if, on the other hand, the downstream pressure is allowed to rise to a sufficiently high value, then the resulting steady-state vapour composition will be determined solely by vapour-liquid equilibrium criteria and hence will be membrane independent. What is very desirable is a simple expression that describes this variation in vapour composition as a function of downstream pressure (and other relevant variables) between those two limiting values. If the vapour steadily issuing from the membrane is removed viscously (that is to say, the vapour is removed without further species separation) then the composition of the vapour removed by the pumping process, which must be identical to that issuing from the membrane, is identical to the steady-state vapour composition p,/p,, so that using eqn. ( 1) : PO Wo” pw &Cw-

(1 -P,/P,“) (1 -P~/P,“)

174

By multiplying both sides with the term (1 -p,/p,“), multiplying out the left hand side bracket, and finally re-arranging, pw is removed from the right hand side leaving just the one variable, po: ~0

Worn

~w

Q&v”’

(1 -PO/P,“)

+PolPw”

It is evident from eqn. (2) that the vapour compositionp,/p, will vary continuously with the total downstream pressure (po+pw) at the vapour/membrane interface, between two limiting values. At a sufficiently low downstream pressure, such thatp, up,” andp, <
175

0.1 DOWNSTREAM

1 VAPOUR

.o

10 PRESSURE

100

(mbar)

Fig. 1. Separation factor as a function of downstream vapour pressure at 25°C calculated using eqn. (2): (a) 0.05% by volume octan-l-01 in water; (b) 10% by volume methanol in water.

but merely to reinforce a broad and comprehensive picture of membrane function. We are aware that such effects as predicted by eqn. (2) have previously been studied in considerable depth and at considerable length [ 3-5,9-161 but, to the best of our knowledge, the basic mathematical description has never been put so succinctly. Of course, as with eqn. (1), eqn. (2) must again be regarded as an approximate membrane equation, since its derivation ignores many complicating features that are known to be frequently associated with the pervaporation process. However, it may be of interest to point out that the model of downstream vapour composition as developed by Greenlaw et al. [101 is easily

-8

-9

1OqO21)

10 (0.21) ION

(in brackets,

I

I

-7

-6

;2:

(

1)

GAUGE

calculated

INDICATION downstream

I

*‘,O1 0

(torr) vapour

pressure,

mbar)

Fig. 2. Separation factor as a function of downstream vapour pressure, measured at 25°C: (a) 0.05% by volume octan-l-01 in water; (b) 10% by volume methanol in water. The ion gauge indication gives the pressure in the mass spectrometer, from which the pressure at the vapour/ membrane interface may be calculated with reasonable confidence.

reduced, without further approximation, to the more manageable form of eqn. (2). This is accomplished by considering the implications of eqns. (16) and (3) in their paper [lo], and hence replacing the x-terms in eqn. (18) with the ratios pillpi and pjl/pjO. Their eqn. (18) is then easily reduced to the form of our eqn. (2) following the steps that we have described. We note that this possibility is confirmed in the work of Brun et al. [ 51 (whose first model is identical in all essentials to that of Greenlaw et al. [lo] ) by consideration of

eqn. (15) in their paper. By implication Brun’s first model is also reducible without further approximation to the form of our eqn. (2). The form of eqn. (2) is therefore retained even when certain simple concentration-dependent diffusion effects are included; hence it has a somewhat broader validity than would appear at first sight. In silicone rubber membrane systems it permits rapid and useful appraisal of pervaporation conditions without the need for the iterative methods used by Greenlaw et al. [lo]. In using membranes for the quantitative sampling and analysis the usual aim is to determine the liquid composition through a determination of the pervaporate (vapour) composition. The relationship between these two compositions is simplest when the separation factor S is constant, since from the definition of the latter, the following linear relationship holds: (3)

POIPW= S~oI~w

Although the membrane separation factor often changes rapidly as the component molar fraction x in the feed liquid changes over the range 0 to 1, for trace components it is often found to be constant over a logarithmically wide range of dilute concentrations. Since trace analysis is of some importance, it is then of interest to use eqn. (2 ) to explore how the separation factor of dilute solutions is likely to change with organic concentration and with temperature, both of these variables entering the equation through the equilibrium vapour pressure terms po” and pw”, over a range of downstream pressures. Of course, temperature also influences the membrane terms D and C”, but in a complex way, so that we normalise to experimentally determined separation factors at low downstream pressures. Figure 3 is the result of such calculations for the toluene/water/silicone rubber system. It seems that to reduce the possibility of errors in such analyses (including errors arising from variations in system total pressure) analyses should be carried out at a sufficiently low pressure, determined by the characteristics of the particular solution being sampled. In some analytical instruments this may involve a loss of signal; in a mass spectrometer this need not necessarily be the case. Clearly eqn. (2) is a useful design equation for these analytical systems. In arriving at eqn. (2 ) viscous flow was assumed at the vapour/membrane interface, a condition that may prevail, especially if a carrier gas is used. Alternatively if molecular flow conditions prevail, such that the mean distance between molecular collisions is determined by the dimensions of the apparatus, then, with the help of kinetic theory, the vapour composition at the vapour/ membrane interface becomes: (l-PO/P,“)

+PJPw”

(4)

Hence. further enrichment near to the membrane can be obtained in favour

I 1.0

0.1

DOWNSTREAM

Fig. 3. Separation trations

VAPOUR

factor as a function of downstream

of toluene in water at two temperatures

I

I

10.0

100.0

PRESSURE

(unbar)

vapour pressure for various volume concen-

calculated using eqn. (2 ).

of high molar mass (M) permeants. In effect the vapour stage in the separation can be used as a further selective membrane, and this is certainly relevant to sampling and analysis applications, although of little relevance to separation processes. The concentration

term

The permeant concentration in the membrane at the liquid/membrane interface is a factor contributing to both the permeation flux (through eqn. 1) and the separation factor (through eqn. 2). It is therefore of some interest to know what determines the concentration magnitude and to what extent the magnitude is predictable. For a given membrane material the permeant concentration in the membrane would be expected to be dependent upon the permeant-polymer mutual solubility, the permeant concentration in the feed solution, as well as such

179

physical variables as temperature and pressure. In this account only the former two variables are considered in detail and it is convenient to consider each in turn, though there is some overlap between them. Permeant-polymer

solubility

In this section we consider the permeant-polymer mutual solubility, the extent to which it may be predicted and the extent to which it influences the separation factor. This problem has been discussed and tackled from a semiquantitative point of view in various ways [2,17], often yielding qualitative correlations between experimental results and the so-called solubility parameters. Although the ultimate value of such correlations is open to question (they appear to do little more than set the rule of thumb “like dissolves like” to an arbitrary numerical scale), two separate techniques of solubility trend prediction are outlined here since they appear to confirm that solubility dominates permeation and separation for a wide range of organics in silicone rubber. The first technique is based on the Scatchard-Hildebrand activity-solubility equation [ 181, from which the following relationship may be extracted for the partition coefficient, P, of a component, o, between an aqueous solution, w, and a membrane, m: P=C,“/C,“=constantXexp~~

[ (6w-do)2-

(6m-So)2]

where (S, - S,,) is the solubility parameter difference between the water and component, 0, (8, - SO)similarly for the membrane, and u, is the molar volume of the component, o. The solubility parameters that we use each have three components, separately quantifying the contribution of dispersion forces, polar forces and hydrogen bonding to the solubility process. The calculation of solubility parameter differences is then achieved in the following way: (6w-60)2=

(&d-6:)2+

(S,“-SOP)“+

(&h-Q)”

where the superscripts refer to the named force components above. In fact, the partition coefficients calculated using the above equation turn out to be far too high so that, in what follows, we restrict ourselves to considering only the exponent term or part of the exponent. The second technique is based on the Flory-Huggins equation, a fairly concise and relevant account of which is given by Treloar [ 191. This relates the volume fraction, V, of a liquid sorbed in a polymer, to its equilibrium vapour pressure, p”, and to the liquid/polymer interaction parameter, x, through the expression: ln(pe/p*) =ln v+ (l-

v)+x(l-

v)2

where p * is the saturation vapour pressure of the liquid. We shall assume that

180

this expression holds for each component of a dilute solution in contact with the polymer, and simplify by considering only the minority component of the solution at dilutions such that v << 1. This approximation is relevant to many trace analysis situations and besides, it leads to simple, experimentally verifiable, predictions. We may then write: v-$exp[-(l+x)]=yrexp[-(1+X)] where the expression p” = yxp * has been used. Hence:

~I~=Yew[--(1+x)l

(7)

We note that the approximate relationship (6) is essentially equivalent to the usual membrane interface equilibrium expression [ 81 obtained by equating the activities of the membrane and feed solution. Equation (6) predicts a linear relationship between membrane concentration and solution concentration for a given binary solution pair, since the activity coefficient y will not be expected to change over the dilute range. More interestingly perhaps, since the separation factor might be expected to be related to the quantity V/X:(the ratio of the permeant concentration in the membrane to that in the solution) then for a range of dilute binary solutions, the separation factor might be expected to be directly related to the activity coefficient y, as well as to the exponential interaction term in x through eqn. (7). Now, on moving upwards through the alcohol homologous series (for example), the alcohol activity coefficient in aqueous solution rises rapidly and by many orders of magnitude, and this trend towards increased sorption would be reinforced by the expected fall in the interaction parameter x between the higher alcohols and the non-polar silicone rubber. Although the dramatic increase in adsorption at solution/solid interfaces, and at a given solution concentration, in ascending homologous series, has long been known [ 201 (giving credibility to eqn. 7), the consequences of this effect on the diffusion of the adsorbed species through the solid has, to the best of our knowledge, not been explored. Hence a homologous series makes for an interesting investigation into the membrane separation factor. Experimental results for the alcohol series in dilute aqueous solution are shown in Table 1, together with solubility parameters taken from Barton [ 211, and approximate infinite-dilution activity coefficients either taken from Gmehling and Onken [22], or else calculated as the inverse of the saturated concentration in aqueous solution [ 231. The results show that the membrane separation factor rises continuously from methanol to decanol with an apparent immunity to molecular length that is rather striking. The common trends in separation factor, activity coefficient and solubility parameter are readily apparent. The two uppermost alcohols were determined at 40°C in order to shorten

181 TABLE 1 Alcohol separation factors, activity coefficients and solubility parameters n-Alcohol

Feed solution concentration (% volume)

Separation factor

Approximate activity coefficient”

Solubility parameter (MPa)“’ Dispersion

Polar

H-bonding

Total

Methanol

1.0

9

2

15.1

12.3

22.3

29.7

Ethanol Propanol Butanol Pentanol Hexanol Heptanol

1.0 1.0 1.0 1.0

17

5 15 50 200 1000

15.8 16.0 16.0 16.0

8.8 6.8 5.7 4.5

19.4 17.4 15.8 13.9

26.0 24.3 23.33 21.7

17.0

3.3

11.9

21.1

0.5 0.1 0.05

Octanol Nonanol Decanol

0.01 0.005

67 74 265 1050 1600 3100 4000

3000 114000

5000

“At infinite dilution.

TABLE

2

Separation

and solubility factors for the range of organic compounds

Compound

Feed solution

Separation

concentration ( % volume )

factor

Methanol

1.0

Ethanol n-Propanol n-Butanol Phenol Acetone Pyridine n-Pentanol Butanone

1.0 1.0 1.0 1.16” 1.0 1.0 1.0 1.0

n-Octanol Nitrobenzene Dichloromethane

9

investigated Solubility

factor

A

B

-2.3

9.2

5.0 13 22 24 35 44 35 50

8.9 8.5 8.2 6.8 3.7 2.5 7.1 2.9

0.05 0.1 0.01

17 67 74 97 170 220 270 750 3100 4200 11000

64 62 36

6.8 2.7 1.2

Tetrachloromethane Chloroform

0.03 0.01

12300 15000

80 50

0.61

Benzene Chlorobenzene o-Dimethylbenzene Toluene

0.1 0.03 0.01 0.01

20000 28000 29000 36000

69 74 88 81

0.011

Ethylbenzene

0.01

43000

97

“Percentage

mass.

182

SOLIJBILITY

FACTOR

A

Fig. 4. Measured separation factors versus calculated solubility factor A for the organics listed in Table II. Dilute solutions were used throughout at 25”C, and the membrane thickness was 0.2 mm.

response times; in common with other investigators we find that changes in separation factors with temperature are relatively small. Moreover, since these two alcohols have very low vapour pressures, eqn. (2 ) indicates that their true membrane separation factors would have to be determined at a downstream pressure of around 0.01 mbar or less. Since our measurements were made at around 0.1 mbar, we suspect that our measured separation factors are rather low. Table 2 lists separation factors from dilute aqueous solutions for all organics that we have so far measured. A 0.2-mm thick silicone rubber membrane was used. The solubility factor A, also in the table, is the full exponent of the partition equation (5), involving the water as well as the membrane and the organic permeant. All solubility parameters were taken from Barton [21] with

183

the exception of that of the silicone membrane for which a three-component solubility parameter has not been found. It was considered appropriate to choose a parameter for the membrane (at least in the first instance) that corresponded approximately to that organic having the highest separation factor in the membrane. Toluene qualified at the time of this analysis (although it has now been displaced by ethylbenzene). The common trends of the separation factor and the solubility factor A are readily apparent in the table, although the correlation falters locally in the lower part. The data are shown graphically in Fig. 4. The logarithmic relationship between the separation factor and the solubility factor A appears to further support the view that it is solubility that dominates the permeation flux through silicone rubber. The third column of Table 2 lists the simpler solubility factor B, where B is given by: u, (8, - S, )‘/RT, involving the organic/membrane interaction only. Note that B is closely related to the interaction parameter x, since x=x+B, where xSis an entropy term often found to have a value of around 0.3 [ 191. The expected inverse relationship with the separation factor now holds, although the correlation again falters, this time towards the middle of the table. Taken all together, the data in Tables 1 and 2 appear to confirm, as far as they go, that it is solubility that strongly determines permeation of organics through silicone rubber, rather than the diffusion coefficient. This conclusion is apparently in agreement with the recent work of Bell et al. [ 241. The solution concentration

In this section we consider how the permeant concentration in the solution determines the concentration within the membrane and the extent to which this influences the separation factor. Although when using a silicone rubber membrane the separation factor is constant over a logarithmically-wide range of dilute solution concentrations [ 251 and often achieves very high values for organic compounds in water, it is invariably found that as the organic concentration in the feed solution increases over the molar fraction range 0 to 0.5, the organic separation factor falls dramatically and often achieves a value not far removed from unity in the molar fraction range 0.5 to 1 [ 7,26,27]. Hence what appears to be a promising membrane performance, as regards magnitude and constancy of separation factor using dilute solutions, often turns out to be much less impressive for separating the more concentrated solutions, a region where many azeotropes exist. From the point of view of sampling and analysis through membranes, a separation factor that falls as the solution concentration rises results in a diminished analytical sensitivity, since the change in vapour composition as a function of change in solution composition, diminishes and may even become stationary (eqn. 3). It is pertinent to ask why this dramatic fall in separation factors occurs. As far as we are aware, no convincing explanation, simple or

184

elaborate, is offered in the membrane literature. For the case of partially miscible tertiary liquid mixtures (for example, ethanol/water/benzene [ 23]), we note that the composition of the two equilibrium phases formed often show a separation factor for a pair of components (based on their concentration ratios in the two phases) that varies in the dramatic manner described above. We presume therefore that the effect is simply a consequence of solubility thermodynamics and below an attempt is made to describe the phenomenon as it applies to silicone rubber in a simple and possibly useful quantitative manner. When using a silicone rubber membrane in conjunction with aqueous organic solutions, experimental investigations can of course be carried out over the complete range of solution concentrations (molar fraction 0 to 1) only for those organic compounds that are completely miscible with (and therefore have considerable affinity for) water. Since silicone rubber is hydrophobic this implies that those same organic compounds will tend to be silicone-phobic, and hence tend to have low concentrations within the silicone rubber throughout the complete range of solution concentrations. When this is the case, then the approximate form of the Flory-Huggins solubility equation as developed in the previous section is applicable. Sorption measurements have been carried out for those normal alcohols (together with butanol) that are miscible with water in all proportions, by immersing the membrane material in the pure alcohol and determining the mass increase. In this process the membrane mass rises to a maximum value after an immersion time that varies from alcohol to alcohol, after which the mass slowly decreases. We presume that this mass decrease is due to the leaching out of fillers, since when the membrane is subsequently dried a net mass loss is found. The data given in Table 3 correspond to the above-mentioned sorption maxima and show that the sorbed mass of alcohols increases as the alcohol series is ascended, as would be expected, and reaches a value of around 12% of membrane mass for butanol. Use of the approximate form of the Flory-Huggins TABLE

3

Sorption in silicone rubber, and van Laar coefficients Compound

Sorption silicone

in

used for the calculation of activity coefficients

van Laar coefficients (base 10 logs)

rubber (g/g)

‘41,

Water

0.0026

-

API -

Methanol Ethanol Propanol Butanol

0.0160 0.0190 0.1200 0.1300

0.312 0.701 1.190 1.760

0.235 0.404 0.549 0.522

185

equation (in which the volume fraction of the sorbed material is small compared with unity) is therefore reasonable at least up to butanol, for attempting to describe separation factor behaviour as a function of solution concentration over the molar fraction range 0 to 1. We note that for dilute organic solutions the approximation will have applicability to a much wider range of organic compounds. Assuming that the two components of the binary solution (water and alcohol in this case) exist in the membrane without mutual interaction (a reasonable assumption at low concentrations in the membrane) then eqn. (7) will hold for each component, and a separation factor may then be defined in terms of the volume fractions in the membrane YJv,, and the molar fractions in the liquid X,/X,: (~J&V)l(%Vl&) =~JcJl&Lv where the exponential polymer-permeant interaction term has been abbreviated to I. The previous equation may easily be converted into a separation factor based on the molar ratios in the two (liquid and membrane ) phases, so that:

where p is density and M is molar mass. Finally, from eqn. (7)) the sorption up from a pure liquid is identical to the interaction parameter I, since under these conditions both y and x are unity; hence the permeant-polymer interaction term is directly measurable in a simple way. The liquid-to-membrane separation factor then becomes: (y,/y,) (&,,,Ix,)

=

y~ovopMw =yomoMw

ww vwpMo ~wmvMo

(8)

where m,/s is the ratio of the masses sorbed, each individually determined using the pure liquid. Equation (8) predicts the separation factor between a binary solution and the membrane, for the case of low component concentrations within the membrane. The separation factor between the solution and the pervaporate vapour will differ from eqn. (8) by the ratio of the diffusion coefficients of the two components. If, for the sake of simplicity, the diffusion coefficient ratio is taken as unity, and assumed not to vary dramatically over the complete solution concentration range (assumptions that are compatible with the low membrane-concentration approximation, compatible with the work of Newns and Park [ 281 in respect of benzene in silicone rubber, and approximately in accord with our own findings described in the following sections of this paper) then the predictions of eqn. (8) may be usefully and directly compared with measurements of pervaporation separation factor.

186

Such comparisons have been made for aqueous solutions of methanol and ethanol (Fig. 5) and for n-propanol and n-butanol (Fig. 6). For each alcohol, the ratio of the sorbed masses, alcohol to water, were determined by silicone rubber immersion in the pure liquids (Table 3); the activity coefficients were calculated using the van Laar equation [ 221; the van Laar coefficients (Table 3) are averaged values of the data given by Gmehling and Onken [ 221. For all four alcohols there is clearly good agreement between calculation and experiment as regards the form of the dependence between separation factor and solution concentration. This form is of course determined entirely by activity coefficient behaviour in the feed solution. For methanol and ethanol

a

18.0

16.0

14.0 METHANOL 12.0 8 L a L ci ;I a : a :

10.0

. 8.0

\ 6.0

MEASURED

4.0

POINTS

2.0

I

0 0

I

I

0.2

ORGANIC

I 0.4

MOLAR

1

I 0.6

I

I 0.8

I

1 1 .o

FRACTION

Fig. 5a. Separation factor as a function of (a) methanol and (b) ethanol molar fraction aqueous liquid phase. The lines correspond to eqn. (8) and the points are experimental taken at 25°C.

in the values

187

b

18.0

16.0

14.0 ETHANOL i?

12.0

: a LL

10.0

z F a

8.0

2 a :

6.0

MEASURED

4.0

CALCULATED

POINTS

LlN\

.

2.0

0 0.2

ORGANIC

0.4

MOLAR

0.6

0.8

1.0

FRACTION

Fig. 5b. (For legend see Fig. 5a).

there is also good agreement between calculation and experiment as regards the magnitude of the separation factor. For n-propanol and n-butanol the agreement in magnitude is clearly not good but those differences may be explained, to some extent, by actual differences in the diffusion coefficients. Further errors probably arise from the mass spectrometer differential sensitivity between organic species, and perhaps because of other approximations used (see Appendix I ) . We conclude that, in these and similar cases, the dependence of the pervaporation separation factor on solution concentration can be quantitatively described to a useful extent using simple expressions derived from solubility thermodynamics, with the feed solution activity coefficients apparently having a dominant effect. In contrast with this approach we note that in a recent paper,

188

Seok et al. [ 261 strongly imply that, in the case of the ethanol/water/silicone rubber system, the dependence is due to membrane swelling. This explanation is not only difficult to quantify, but it is also difficult to justify since our measurements reveal negligible swelling in that system. Of course, in those systems where significant swelling occurs, solution thermodynamics would still be expected to hold [ 191, although diffusion coefficients would be expected to change significantly. In this connection we note that Brun et al. [ 51 have reproduced a similar functional dependence of separation factor on solution concentration using an elaborate multi-parameter model. The authors appear to make no statement concerning the question of whether, or to what extent, the depen1000

a

PROPANOL

MEASURED

I

1 0

I

I

ORGANIC

Fig. 6a. Separation

I 0.4

0.2

MOLAR

I

POINTS

I 0.6

I

I

0.8

I

I 1.0

FRACTION

factor as a function of (a) n-propanol

aqueous liquid phase. The lines correspond taken at 25°C.

=

and (b) n-butanol molar fraction in the

to eqn. (8) and the points are experimental

values

189

-b

BUTANOL

I OC

CALCULATED

10

MEASURED

LINE

POINTS . .

I

1 0

1

I

0.2

I 0.4

ORGANIC

MOLAR

I

I 0.6

I

. 0.6

I

1 1 .o

FRACTION

Fig. 6b. (For legend see Fig. 6a).

dence in their case arises from activity coefficient behaviour external to the membrane, or diffusion coefficient behaviour within the membrane. The diffusion coefficient

From the point of view of sampling and analysis, the immediate significance of the diffusion coefficient D is that it determines the response time of the analysis. An immediate problem is that a literature search has revealed diffusion coefficients for only seven organics in silicone rubber [ 29,30,31], as listed in Table 4. These show a marked lack of variation between the organic species listed.

190 TABLE 4 Published diffusion coefficients in silicone rubber Compound

Diffusion coefficient

Temperature (“Cl

Reference

Dx~O'~ (m*-set-I) Benzene

2.80

25.0

28

Halothane” Etbraneb

1.80 1.52

30.5 30.1

30

n-Pentane

2.18 4.48 2.83 5.44 4.81

30.0 30.0 30.0 30.0 30.0

31

Neo-pentane n-Butane Iso-butane

“2-Bromo-2-chloro-l,l,l-trifluoroethane. b2-Chloro-l,1,2-trifluoroethyldifluoromethylether.

The time t,,, elapsed between a step change in concentration at the liquid/ membrane interface, with the membrane initially permeant-free, to the point at which the permeation flux achieves half of its ultimate steady-state value, is given by the expression [ 321: t1,2 = 12/7.2D

(9)

where I is the membrane thickness. For a 50 pm thick silicone membrane, eqn. (9) yields response times of the order of 1 set for the organics listed in Table 4. With care such response times can actually be achieved. In using a mass spectrometer for the study of membranes, the transient permeation characteristic for a single identifiable permeant may be directly obtained by keeping the instrument tuned to the relevant mass number. In this way diffusion coefficients of permeant species may be obtained by the direct experimental determination of tllz and hence calculating D using eqn. (9). In this way we have determined the diffusion coefficients for all members of the alcohol homologous series up to decanol, using dilute aqueous solutions. To be certain that we were measuring membrane response times, as opposed to instrument response times (adsorption of organics onto the walls of vacuum vessels in well known, giving rise in our case to spurious response times), a membrane thickness of 0.8 mm was used, and the measurements were carried out at 80 -t 3 ‘C. These values were chosen after much preliminary experimentation; for example, Fig. 7 shows how the measured ethanol response time tllz varied with membrane thickness at 80” C for the solution ethanol/water (10% v/v).

191

The alcohol diffusion coefficients are listed in Table 5 and they show a steady, though hardly dramatic, fall as the series is ascended. The difference in the coefficient for methanol and decanol is about a factor of 4. The most likely errors in our measurements would arise from the adsorption of the organics on the vacuum walls as they issue from the membrane, and from the questionable validity of eqn. (9) for the range of solution concentrations indicated in Table 5, bearing in mind that its derivation assumes instantaneous chemical equilibrium at the liquid/membrane interface at time t= 0. Both of these errors would tend to produce smaller diffusion coefficients for the higher alcohols. Hence

(THICKNESS;

(“mf

Fig. 7. Measured response times tIlz as a function solution 10% by volume ethanol in water at 80°C.

of the square of membrane

thickness

for the

192 TABLE

5

n-Alcohol

and water diffusion coefficients

in 0.8 m thick silicone rubber at 80 + 3 ‘C

Compound

Feed solution concentration (% volume)

Diffusion coefficient D x 10”’ (m2-sec-1)

Water Methanol

99.0 1.0

12.0 10.0

Ethanol Propanol Butanol Pentanol Hexanol

1.0 1.0 1.0 1.0

7.1 6.2 5.5 5.1 4.2

Heptanol Octanol Nonanol Decanol

0.5 0.1 0.05 0.01 0.005

4.1 3.9 3.0 2.5

the factor 4 difference between methanol and decanol in our results is, if anything, exaggerated. These results therefore show, under the measurement conditions indicated, a rather small variation in diffusion coefficient, and hence appear to confirm the dominance of solubility in determining permeation flux. Diffusion theory Membrane diffusion theory [ 331 appears to be concerned with the ability of the polymer to physically accommodate the permeant, and to continually provide opportunities, in the form of randomly generated voids, for the permeant to progress (diffuse) through the polymer. Much experimentation has complemented the theory by being primarily concerned with the size of the permeant, the physical qualities of the polymer, and the usual physical variables. Where organic permeants have been used, they have very often been simple alkanes or fairly mundane variants. The exception to this of course has been in the field of dyeing [ 341. Broad systematic exploration of the chemical dependence of the diffusion process is, as far as we can tell, completely absent from the membrane literature; if this is true, it is rather surprising in view of the interest in membranes as chemical separators. The membrane literature therefore appears to have nothing to say concerning the relative diffusion coefficient of, e.g., ethanol and ethylene glycol in silicone rubber, or in any other polymer for that matter. Diffusion theory might suggest that, since both molecules are straight chain and of approximately equal length, they would have similar diffusion coefficients. Our results indicate that their diffusion coefficients differ. under the

193

conditions shown in Table 6a, by about a factor of 7; that is considerably more than the factor difference between ethanol anddecanol. Table 6b lists our measured diffusion coefficients for four straight-chain molecules of approximately equal length; they show considerable variation, for which conventional diffusion theory offers no easy explanation. In Table 6b the coefficient for l-aminobutane is an averaged figure since at low solution concentrations and at room temperature, it changes as the initial permeation proceeds. This is detected by the difference in D calculated using eqn. (9)) which applies to the early and middle stages of the transient process, and that calculated by measuring the maximum slope of the transient process (Appendix III), which is relevant to the later stages. The diffusion coefficient calculated using this latter method is bracketed in Table 6b and indicates a significant increase in D for l-aminobutane as the initial permeation process develops. These differences tend to disappear as the temperature is increased (Table 6~). It seems possible to explain these effects in the following qualitative manner. We suppose that the diffusion process in silicone rubber is not dominated by permeant size effects, but is influenced to a significant extent by specific site, permeant-polymer interactions. The diffusion process may then be likened to a three-dimensional dynamic adsorption process in which the permeant moves from adsorption site to adsorption site, where the dwell time 7 at each site is determined by the strength of the permeant-polymer interaction through the expression [ 351: 7= 7, exp (E/RT). E is the activation energy characterising the permeant-polymer physi-sorption bond and l/7, is the vibrational frequency of the bond. If we now take the fundamental expression for the diffuTABLE 6 Diffusion coefficients for various organics of similar length in 0.8 mm thick silicone rubber Compound

Feed solution concentration (% volume)

Diffusion coefficient Dx 10” (m2-set-I)

Temperature (“Cf3”C)

a. Ethanol Ethylene glycol

30 30

12 1.8

80 80

b. n-Pentane Butanone n-Butanol 1-Aminobutane

0.05 1.0 1.0 1.0

3.9 (5.1) 2.5 (4.0) 0.65 (0.93) 0.33 (0.85)

26 30 30 30

c. n-Butanol 1-Aminobutane

1.0 1.0

5.5 (7.6) 2.3 (3.3)

80 80

194

8.0

a METHANOL

7.0

;y 0

6.0

-0

0

1

0

0.6

0.4

0.2

ORGANIC

MOLAR

0.8

1.0

FRACTION

Fig. 8a. (for legend see fig. 8d).

sion coefficient 0=11’/2r, where ;1 is the jump length, and interpret r as the dwell time at each adsorption site (rather than the time taken to move between sites ) we then obtain: (10) This equation is identical to that which forms the basis of conventional polymer diffusion theories, but with the important difference that the interpretation of E and z, now intimately concerns the permeant molecule. We assume that the amine functional group in 1-aminobutane interacts strongly through hydrogen bonding with a specific site (the oxygen, perhaps) in silicone rubber and is temporarily held (adsorbed) with a large activation energy E. Hence the diffusion coefficient is initially small. As the diffusion process proceeds these specific sites are filled, and subsequent permeant molecules diffuse at a greater rate since the density of strongly interacting sites

195

8.0

b ETHANOL

7 .o In .

“E

6.0

0 -0 rx

5.0

5 w 3

D

.

slope .

4.0

i; IL 0” 0

3.0

E v, 1 LL LL n

2.0

1 .o

0

I

I

I 0.2

ORGANIC

I 0.4 MOLAR

I

I 0.6

I

I 0.8

I

1 1 .o

FRACTION

Fig. 8b. (for legend see fig. 8d).

has diminished. Additionally, as the temperature is increased, dwell times at each site diminish in the usual way (eqn. lo), the strongly interactive sites become less important, and the diffusion coefficient increases. We are aware that some of the experimental phenomena under discussion here are well known and are normally interpreted in terms of dual sorption theory [ 36 ]. However, the emphasis in our interpretation bears a much closer resemblance to the specific sorption-site model of diffusion as forwarded many years ago by King ]371. Of course, we are not suggesting that eqn. (10) replaces conventional diffusion theory. Our purpose is merely to emphasise the possibility that Van der Waals-type interactions might in fact play a significant role in the diffusion process, especially in silicone rubber and perhaps in other polymers too. After all, during the formative years of diffusion theory, these possibilities were clearly accepted, though supported by very limited experimental data [38]; subsequent developments in diffusion theory have rather successfully disguised such

196

8.0

‘C

PROPANOL

_ u)

7.0

“E 0

6.0

-0 ?c Li

5.0

W 3 c

k

4.0

0 0 z 0, 3 LL LL a

3.0 .

Dll2

2.0

1 .o

I

0 0

I

I

0.2

I

I

0.4 ORGANIC

I 0.6

MOLAR

I

I 0.8

I

I 1 .o

FRACTION

Fig. 8~. (for legend see fig. 8d).

possibilities, and no further experimental work appears to have been carried out. Concentration-dependent diffusion coefficients Newns and Park [ 281 found the diffusion coefficient of benzene vapour in silicone rubber to be remarkably constant, although only a limited concentration range was studied. Barrie and Platt [39] found that the diffusion coefficient of water vapour in silicone rubber decreased significantly with increasing water concentration in the membrane. A very similar trend was found for methanol in silicone rubber [ 401. In detail our results, measured using binary solutions, differ from all those just mentioned. Using the direct permeation transient technique as outlined previously, the diffusion coefficients for the alcohols from methanol to butanol, and that for water, were determined using a wide range of aqueous binary solution concen-

197 a.0

d

(0 .

NE

BUTANOL 7.0

1

x

1

6.0

-

5.0

-

4.0

-

3.0

-

I2 W E iL ii

0 cl z v, 3 LI LL

2.0

L__------

slope _ _ ---,-

L-_-_-w--

___--

*_____----

D

__C__-

___-

0

Dll2

1 .a

t Ol

I

0

I

I

0.2

I 0.4

ORGANIC

I

I 0.6

MOLAR

I

I

0.6

I

I 1 .o

FRACTION

Fig. 8. Alcohol diffusion coefficients as a function of (a) methanol, (b) ethanol, (c) n-propanol and (d) n-butanol molar fraction in the aqueous liquid phase at 25°C. Dl12 refers to the determination using the time taken for the permeation transient to reach one-half of the final steady value (eqn. 9 ) . DsLo, refers to the determination using the maximum slope of the transient function (Appendix III).

trations. These results are summarized in Figs. 8a-d and show that, for the alcohols, the diffusion coefficient increases as the alcohol concentration in solution increases, with a marked increase over the low concentration range. The magnitude of the concentration-dependent increase diminishes on going from methanol to butanol. The water diffusion coefficient has a value around 3 X lo-” m2/sec in all cases. We tentatively interpret these results by proposing, in accord with the discussion in the previous section, that at low alcohol concentrations, permeantpolymer interaction dwell-times are relatively long, giving rise to a relatively slow diffusion process. As the alcohol concentration increases an increasing number of these interaction sites tend to be filled, enabling subsequent permeant molecules to diffuse at a greater rate.

00 0

0.1

0.2 MEMBRANE

0.3

0.4 THICKNESS

Fig. 9. Measured separation factor as a finction volume toluene in water at 25°C.

The membrane

0.5

0.6

0.7

(mm)

of membrane thickness for the solution 0.01% by

thickness

It is possible to envisage conditions under which the membrane diffusion flux as given by eqn. (1) could not be adequately supplied by the arrival flux from the bulk solution. Under such conditions, eqns. (1) and (2 ) would apply to the depleted and unknown solution in contact with, and possibly still in chemical equilibrium with, the membrane face. The resulting separation factor would not apply to the solution as a whole. The probability of such an effect occurring would be expected to increase as one moved to organics of increasing membrane solubility, and/or to membranes of decreasing thickness, and/or to solutions of decreasing organic concentration and/or to higher fluxes caused by higher (or possibly lower) temperatures. The effects has traditionally been overcome by solution agitation. An alternative method is simply to increase the membrane thickness thereby reducing the flux drain on the liquid, although this increases the response time. The above views appear to be confirmed by experiment: methanol and ethanol, both having a relatively low solubility in silicone rubber, and hence a relatively low membrane flux, show little change in separation factor down to a membrane thickness of around 50 pm, whereas toluene, with a solubility in

199 SAMPLE

FLOW

SYSTEM

I

I/

I

MEMBRANE

CUP

-- .......-L AMEMBRANE -

POROUS

63

HOKE

SUPPORT

B SEALS

VALVES

MASS

SPECTROMETER b

\/

/I-

@-METROSIL AND

PUMP

Y

VACUUM SAMPLE(PL)

Smm

GOLD

LEAK

PIPE dia.

t ROTARY

PUMP

Fig. 10. Equipment schematic.

TABLE 7 Separation factors from dilute aqueous solutions at two temperatures Compound

Methanol Phenol Pyridine Toluene

Feed solution concentration ( % volume )

25°C

42°C

Membrane thickness (mm)

1.0 1.16” 1.0 0.01

9 91 220 44000

8 120 220 41000

0.2 0.2 0.2 0.6

“Percentage mass.

Separation factor

(restrictors)

200

silicone of probably one thousand times that of methanol, and hence a relatively high membrane flux, shows a dramatic change in separation factor with membrane thickness (Fig. 9). All solutions were vigorously agitated in the membrane cup system (Fig. lo), the essential point being that on the plateau agitation has little or no effect. Hence the widely held view that separation is not thickness dependent must be treated with caution in practical situations. This point has been discussed by Hwang and Kammermeyer [ 411. Temperature effects

Since all terms (apart from membrane thickness) in the permeation eqn. (1) are strongly temperature dependent, it is to be expected that the permeation flux will show considerable temperature sensitivity, and this has been confirmed in numerous studies. However, since the vapour composition ratio is given by the ratio of two diffusion coefficients and the ratio of two solubility terms (eqn. 2 ), we might expect, as a first approximation, that the membrane separation factor will be relatively temperature independent. Limited experimental results (Table 7) appear to confirm this view, but only as long as the membrane thickness is sufficient to completely avoid causing solution depletion effects as the temperature is changed. Numerous reports support these views (e.g. [2]). Conclusions

We have explored in a broad manner numerous variables relevant to the pervaporation of organic compounds through silicone rubber. Our findings suggest that a useful framework of understanding of silicone rubber membrane function can be achieved by the application of simple arithmetic together with familiar concepts concerning the thermodynamics of solubility. Simple and approximate expressions are derived relating separation factor to downstream vapour pressure and to upstream solution concentration. Additionally, our results appear to confirm that organic solubility in the silicone membrane is the major factor determining the pervaporation flux, and apparently reveal the influence of permeant-polymer interactions on the diffusion coefficient. Acknowledgements

This work was supported by the Science and Engineering Research Council (SERC); the mass spectrometer was made available for the duration of the work by VG Gas Analysis Ltd, ICI Chemicals and Polymers Group provided financial assistance; Miss Geraldine Smith of this Department helped generously throughout. We are indebted to Professor P. Meares for critically commenting on this work.

201

List of symbols

C D > K 1 ii 0 P P* P R i t T u W

x i V

X

P

concentration ( mol/m3) diffusion coefficient (m2/sec) superscript denotes equilibrium permeation flux (mol/m2-set) constant membrane thickness (m) subscript or superscript denotes membrane molar mass subscript denotes organic pressure saturated vapour pressure partition coefficient gas constant (J/K) subscript denotes saturated condition separation factor time (set) temperature (K) molar volume ( ml/m01 ) subscript or superscript denotes water liquid molar fraction activity coefficient solubility parameter (MPa) “’ volume fraction of sorbed liquid interaction parameter density

References 1

2

3 4

5

B.J. Harland, P.J.D. Nicholson and E. Gillings, Determination of volatile organic compounds in aqueous systems by membrane inlet mass spectrometry, Water Res., 21 (1987) 107-113 (Contains references to earlier work). P. Aptel and J. Neel, Pervaporation, in: P.M. Bungay, H.K. Lonsdale and M.N. de Pinho (Eds.), Synthetic Membranes: Science, Engineering and Applications, Reidel, Dordrecht, 1986, pp. 403-436. J. Neel, P. Aptel and R. Clement, Basic aspects of pervaporation, Desalination, 53 (1985) 297-326. R.A. Shelden and E.V. Thompson, Dependence of diffusive permeation rates on upstream and downstream pressures. III. Membrane selectivity and implications for separation processes, J. Membrane Sci., 4 (1978) 115-127. J.-P. Brun, C. Larchet, R. Melet and G. Bulvestre, Modelling of the pervaporation of binary mixtures through moderately swelling, non-reacting membranes, J. Membrane Sci., 23 (1985) 257-283.

202 6

8

C.E. Rogers, Permeation of gases and vapours in polymers, in: J. Comyn (Ed.), Polymer Permeability, Elsevier Applied Science Publishers, Barking, 1985, pp. 11-73. K. Ishihara, Y. Nagesse and K. Matsui, Pervaporation of alcohol water mixtures through PTMSP, Makromol. Chem. Rapid Commun., 7 (1986) 43-46. C.H. Lee, Theory of reverse osmosis and some other membrane permeation operations, J.

9

Appl. Polym. Sci., 19 (1975) 83-95. T.Q. Nguyen, Modelling of the influence of downstream

7

10

11 12

13

14

pressure for highly selective perva-

poration, J. Membrane Sci., 34 (1987) 165-183. F.W. Greenlaw, R.A. Shelden and E.V. Thompson, Dependence of diffusive permeation rates and selectivities on upstream and downstream pressures. II. Two component permeant, J. Membrane Sci., 2 (1977) 333-348. R. Rautenbach and R. Albrecht, Separation of organic binary mixtures by pervaporation, J. Membrane Sci., 7 (1980) 203-223. F.W. Greenlaw, W.D. Prince, R.A. Shelden and E.V. Thompson, Dependence by diffusive permeation rates on upstream and downstream pressures. I. Single component permeant, J. Membrane Sci., 2 (1977) 141-151. R.A. Shelden and E.V. Thompson, Dependence of diffusive permeation rates and selectivities on upstream and downstream pressures. IV. Computer simulation of non-ideal systems, J. Membrane Sci., 19 (1984) 39-49. H.F. Knight, A. Duggal, R.A. Shelden and E.V. Thompson, Dependence of diffusive permeation rates and selectivities on upstream and downstream pressures. V. Experimental results for the hexane/heptane (ideal) and toluene/ethanol (non-ideal) systems, J. Membrane Sci.,

15

26 (1986) 31-50. A. Duggal and E.V. Thompson, Dependence of diffusive permeation rates and selectivities on upstream and downstream pressures. VI. Experimental results for the water/ethanol sys-

16

tem, J. Membrane Sci., 27 (1986) 13-30. J. Neel, Q.T. Nguyen, R. Clement and D.J. Lin, Influence of downstream pressure on the pervaporation of water-tetrahydrofuran mixtures through a regenerated cellulose membrane

17

(cuprophan), J. Membrane Sci., 27 (1986) 217-232. B. Schneier, Use of Gee relationship in a diffusion study, J. Appl. Polym. 2243-2352.

18 19 20 21

Sci., 16 (1972)

J.H. Hildebrand, J.M. Prausnitz and R.L. Scott, Regular and Related Solutions, Van Nostrand Reinhold Co., New York, NY, 1970. L.R.G. Treloar, The Physics of Rubber Elasticity, Oxford University Press, Oxford, 1975, Chap. 7. R.S. Hansen and R.P. Craig, The adsorption of aliphatic alcohols and acids from aqueous solutions by non-porous carbons, J. Phys. Chem., 58 (1954) 211-215. A.F.M. Barton, Handbook of Solubility Parameters and Other Cohesion Parameters, CRC Press, Boca Raton, FL, 1983.

22

J. Gmehling and U. Onken, Vapour-Liquid CHEMA, Frankfurt, (1977).

23

H. Stephen and T. Stephen (Eds.), gamon Press, Oxford, 1964.

24

C.M. Bell, F.J. Gerner and H. Strathmann, Selection of polymers for pervaporation membranes, J. Membrane Sci., 36 (1988) 315-329. L.W. Tetler, Unpublished results. See also Ref. [ 11. D.R. Seok, S.G. Kang and S.-T. Hwang, Use of pervaporation for separating azeotropic mixtures using two different hollow fiber membranes, J. Membrane Sci., 33 (1987) 71-81. S.A. Leeper, Membrane separations in the production of alcohol fuels by fermentation, in:

25 26 27

W.C. McGregor (Ed.), Membrane NY, 1987, pp. 161-200.

Equilibrium

Solubilities

Separations

Data Collection,

Vol. 1, Part 1, DE-

of Inorganic and Organic Compounds,

in Biotechnology,

Per-

Marcel Dekker, New York,

203 28 29

30 31 32

33 34 35 36 37 38 39 40 41 42 43

A.C. Newns and G.S. Park, The diffusion coefficient of benzene in a variety of elastomeric polymers, J. Polym. Sci., 22C (1967) 931-937. G.S. Park, Transport principles, solution, diffusion and permeation in polymer membranes, in: P.M. Bungay, H.K. Lonsdale and M.N. de Pinho (Eds.), Synthetic Membranes: Science, Engineering and Applications, Reidel, Dordrecht, 1986, pp. 57-107. R. Fielding and R.F. Salamonsen, Permeation of halothane and ethrane in silicone rubber, J. Membrane Sci., 5 (1979) 327-338. R.M. Barrer, J.A. Barrie and N.K. Raman, Solution and diffusion in silicone rubber, Polymer, 3 (1962) 595-603. K.D. Zeigel, H.K. Frensdorff and D.E. Blair, Measurement of hydrogen isotope transport in poly (vinyl fluoride) films by the permeation-rate method, J. Polym. Sci., 7 (A-2) (1969) 809819. H.L. Frisch and S.A. Stern, Diffusion of small molecules in polymers, Crit. Rev. Solid State Mater. Sci., 11 (1983-84) 123-187. R.H. Peters, Kinetics of dyeing, in: J. Crank and G.S. Park (Eds.), Diffusion in Polymers, Academic Press, New York, NY, Chap. 9. J.H. de Boer, The Dynamical Character of Adsorption, Oxford University Press, Oxford, 1968. W.R. Vieth, J.M. Howell and J.H. Hsieh, Dual sorption theory, J. Membrane Sci., 1 (1976) 177-220. G. King, Permeability of keratin membranes to water vapour, Trans. Faraday Sot., 41 (1945) 476-487. S. Glasstone, K.J. Laidler and H. Eyring, The Theory of Rate Processes, McGraw-Hill, New York, NY, 1941, Chap. 9. J.A. Barrie and B. Platt, The diffusion and clustering of water vapour in polymers, Polymer, 4 (1963)303-313. J.A. Barrie, Diffusion of methanol in polydimethylsiloxane, J. Polym. Sci., 4 (A-l) (1966) 3081-3088. S.-T. Hwang and K. Kammermeyer, Membranes in Separations, John Wiley Publishers, New York, NY, 1975. A. Cornu and R. Massot, Compilation of Mass Spectral Data, Heyden Press, London, 1975. H.A. Daynes, The process of diffusion through a rubber membrane, Proc. Roy. Sot., 97A (1920) 286-307.

Appendix I

The membrane sampling system (Fig. 10) was interfaced to a VG mass spectrometer via metrosil and gold leaks. Solutions were either placed in the membrane cup and stirred, or else used in a continuous flow system attached to the cup. Total vapour pressure in the sampling system was varied by varying the pumping pipe length, or else closing the pumping valve. Membrane separation factors were normally determined at total pressures of around 0.1 mbar at the membrane. A silicone rubber membrane of 0.2 mm thickness was used, unless otherwise indicated. All membranes were supplied by ESCO (Rubber) Ltd., Lampton Road, Hounslow, Middlesex TW3 4EE, U.K. All measurements were made at room temperature: 25 +- 3’ C, unless otherwise indicated. Solutions of up to 1% organic volume were used unless otherwise indicated. No significant variation in separation factor with concentration was found up to the 1% level.

204

The vapour ratio in the sampling system was taken as the organic principal peak signal divided by the mass 18 signal. The separation factor was obtained by dividing the vapour ratio by the organic molar ratio in the solution. Note that separation factors determined in this way will be different from actual separation factors by an amount dependent upon the sensitivity variation between molecular species in the mass spectrometer. In this paper no attempt has been made to correct for this effect since, where comparisons are possible, our results appear to be similar to those of other workers using different techniques. The sensitivity data given by Cornu and Massot [ 421 suggest that the error in our results will be, in most cases, less than a factor of 2. There is however a notable step change in sensitivity between propanol and butanol due to the highly populated fragmentation pattern of the latter compared with that of the former. This effect gives rise (in the case of butanol) to a principal ion peak of relatively small intensity compared with the total fragmentation intensity and apparently goes some way to explaining the relatively low separation factor of butanol in our measurements, compared with that indicated by calculation. Appendix II The solubility of water in the membrane was determined by immersing membrane material in water for around 200 hours and attributing the resulting mass increase to water absorption. In this way, CWm was determined to be around 250 mol/m3. The solubility of octanol in the membrane was determined by immersing membrane material in a solution of 0.05% volume octanol/water and attributing the mass increase in part to the same quantity of water absorbed in the first measurement, the remainder assumed due to octanol. In this way, G” was found to be around 130 mol/m”. The ratio of the diffusion coefficients was taken from our measurements, giving in the case of octanol D,/ D, = 0.33. The equilibrium vapour pressure for water was taken as 32 mbar, and for octanol in the said solution, 0.12 mbar. The equilibrium vapour pressure for methanol in a 10% volume methanol/water solution was taken as 20 mbar. Appendix III From Daynes [ 431, the permeant flux egressing at the vapour/membrane interface is given by: JIJ,,,=1+2

C (-l)“exp(

--n2rc20t/Z2)

(11)

n=l

By differentiating this function twice with respect to time and equating the result to zero, the time t,,, at which maximum slope occurs is found to be given

205

Z2/1.1047r2D.Substituting the expression for t,,x into the first differential of eqn. (11 ), the maximum slope of the egress function is found to be 5.91 D2/12=l/tslope. Hence D=12/5.91 tslope. The egress function is qualitatively illustrated in Fig. Al. by t,,x =

I A ------

, __ ;_

I

--

-

I / /

TIME

Fig. Al. Sketch of the permeate egress function, eqn. (11).