Functional polymers and supramolecular compounds for chemical sensors

Synthetic Metals, 61 (1993) 37-45

37

Functional polymers and supramolecular compounds for chemical sensors K.D. Schierbaum

and W. GOpel

Institute of Physical and Theoretical Chemistry, University of Ti~bingen, Auf der Morgenstelle 8, D-72076 Ti~bingen (Germany)

Abstract

We present experimental data and theoretical concepts for the use of functional polymers and supramolecular compounds as layer materials of chemical sensors with high selectivities to monitor organic solvent molecules in air. Polysiloxanes and calixarenes, in particular, serve as model substances in this study. The bulk dissolution of solvent molecules into the polysiloxane layers leads to characteristic sensor signals of quartz microbalance, thermopile and interdigital capacitor transducers. Selectivities can be understood from a simple thermodynamic approach which correlates the partition coefficients of the solvents with the Gibbs enthalpy of dissolution. Surface effects of sensor signals from quartz microbalance transducers which have been coated with calixarene layers are studied as a function of temperature, partial pressure and thickness. Comparative results obtained from thermodesorption spectroscopy and force-field calculations show that specific key-lock interactions occur between calixarenes and solvent molecules.

1. Introduction

Chemical sensors are devices which convert a chemical state as input signal, i.e., the concentration, partial pressure or activity of particles such as atoms, molecules or ions, into an electrical output signal [1]. Usually, they contain a chemically sensitive and selective layer for the specific recognition of particles and a transducer which generates the electrical signal. In addition, filters

Sensor c honges of moss ternperoture thickness

Parlicles:

Organic Solvent molecules

ller

Recognito3: Polysiloxanes Colixorenes

Trar~ducer:

Electronics

BAW's, SAW's Thermopiles Optical transducers Interdigital capacitors

Electrical

signol: Am AT 6d AC

Fig. 1. Key-lock arrangement of a typical chemical or biochemical sensor to detect atoms, molecules or ions ('particles') in the gas or liquid phase. Additional components of 'real' sensors are also indicated.

0379-6779/93/$6.00

or membranes may be used to exclude interfering particles (Fig. 1). The quantitative determination of molecules in the gas and liquid phase by means of chemical sensors requires their interaction with the chemically sensitive layer to be thermodynamically controlled. Under these conditions surface and bulk concentrations of molecules in the layers are adjusted unequivocally by their partial pressures and by the temperature. Layers of polymers and organic cage compounds gain increasing interest as 'model systems' to be used for chemical sensors [2, 3]. They show a large flexibility for tailoring recognition structures with the aim of a specific detection of ions and molecules. Of particular interest in this context is the detection of organic solvent molecules (Table 1) in air with polysiloxanes and calixarenes as sensitive coatings (Table 2). Different transducers may be applied to monitor the solvent-layer interaction by means of mass changes Am (with bulk, surface arid plate acoustic wave devices [4]), temperature changes AT (with calorimetric devices [5]), thickness changes Ad (with optical devices [6]) and capacitance changes AC (with interdigital electrode capacitors [7]). Using these transducers, the experimental work presented in this paper focuses on systematic studies of different 'model systems', i.e., polysiloxanes with nonpolar and polar side groups and calixarenes with different ring sizes and functional groups. Different sensor parameters (Am, AT, fix/ and AC) and interaction

© 1993- Elsevier Sequoia. All rights reserved

38 TABLE 1. Physicochemical properties of solvents used in this study~ Tb (K)

pO (Pa)

M-/~

AS,° (kJ/mol)

AG~°

I/ (cm3/mol)

8~

X

399 342 374

87 727 230

34.6 29.6 31.7

86.6 86.6 84.8

10.96 5.96 8.56

162.7 130.8 127.0

7.12 7.35 7.72

0.04 0.01 0.01

394 334 350

90 935 555

34.8 29.4 29.9

88.3 88.0 85.5

10.69 5.38 6.57

102.4 80.2 96.4

9.01 9.36 8.61

0.43 0.51 0.22

384

172

32.0

83.4

9.23

106.4

8.48

0.19

341

769

29.2

85.6

5.82

140.7

7.04

0.06

351

701

27.2

77.5

6.03

99.0

8.14

0.07

1. Aliphatic compounds

n-Octane, CsH18

n-Hexane, C6H14 Methylcyclohexane, Me-C6Hll 2. Chlorinated compounds

Perchloroethylene, C2C14 Chloroform, CHCI3 Tetrachloromethane, CC14 3. Aromatic compounds

Toluene, Me-~ 4. Ether

Diisopropylether, (i-Pr)20 5. Amines

n-Butylamine, n-BuNH2

"Tb is the boiling temperature at p = 105 Pa; pO the saturation evaporation pressure at T= 298 K; AH° (AS°, AG,°) the molar standard enthalpy (entropy, Gibbs enthalpy) of evaporation at T= 298 K; V the molar volume at T= 298 K and p = 105 Pa; 51 the Hildebrandt parameter as calculated from ~1= (M-/~°/l~m)°'5 (in units (cal/cm3)°'5); X the Flory-Huggins parameter for mixtures with PDMS (see Appendix).

TABLE 2. Polysiloxanes and calixarenes investigated in this study

Polydimethylsiloxane, PDMS Polycyanopropylmethylsiloxane, PCMS Polymethylphenylsiloxane, PMPD Chirasil-Val

R

R'

Me Me Me Me

Me (CH2)3CN C6H5 CH2-CH(CHa)--CO-NH--C(Me) (i-Pr)--CO-NH-t -Bu

25,26,27,28-Tetrahydroxycalix[4]arene 5,11,17,23-Tetra-iso-propyl-25,26,27,28-tetrahydroxycalix[4]arene (i-propyl-calix[4]arene) 5,11,17,23-Tetra-tert-butyl-25,26,27,28-tetrahydroxycalix[4]arene (t-butyl-calix[4]arene) 5,11,17,23-Tetra-t ert-butyl-25,26,27,28-tetrakis-(ethoxycarbonyl-methyloxy)-calix[4]arene 5,11,17,23-Tetra-tert-butyl-25,26,27,28-tetrakistrimethylsilyloxycalix[4]arene 5,11,17,23,29,35-Hexa-tert-butyl-37,38,39,40,41,42-hexahydroxycalix[6]arene 5,11,17,23,29,35,41,47-Octa-tert-butyl-49,50,51,52,53,54,55,56-octa-hydroxycalix[8]arene

mechanisms (e.g., surface adsorption, bulk dissolution) are optimized to detect sensitively and selectively different organic molecules. The theoretical work presented here aims at a thermodynamic and atomistic understanding of experimental data as a prerequisite for future tailoring of new materials for chemical sensors.

2. Experimental Spin-on coating is used to prepare thin polysiloxane layers on quartz microbalance, calorimetric and capacitance transducers. Thermal evaporation under ultrahigh vacuum conditions is used to prepare calixarenes

on a quartz microbalance and surface acoustic wave devices. Details have been published earlier [6]. The transducers to monitor changes of mass Am, temperature AT and capacitance AC consisted of polished quartz microbalance oscillators (10 MHz with Au electrodes, Kristall-Verarbeitung, Neckarbischofsheim, Germany), surface acoustic wave devices (200 MHz, Siemens, Erlangen, Germany), thermopiles with 64 individual Cu/CuNi thermocouples integrated on thin polymer foils (Isabellenhiitte, Heusler G m b H KG, Dillenburg, Germany) and interdigital capacitor structures with Au electrodes and 5/~m electrode distance (Fraunhofer-Institut f-fir Festk6rper-Technologie, Munich, Germany). Details about the experimental setups have been reported earlier [6].

39 3. Results and discussion

3.1. Recognition sites in polysiloxanes and calixarenes The weak molecular interaction mechanisms (Fig. 2) between polysiloxanes or calixarenes and solvent molecules result from short-range van der Waals 'bonds' (due to dispersion forces between polarizable atoms or molecules, forces between polar molecules with permanent dipole moments and polarizable atoms or molecules, and forces between polar molecules) and long-range electrostatic 'bonds' (due to point charges attributed to the differently electronegative atoms in the solvent molecule and in the polysiloxane or calixarene) [8]. To a first approximation, the different interaction forces are additive, i.e., the total binding energy is given by the sum over individual binding energies from all interacting atoms. In this first approximation, corresponding equilibrium distances between interacting molecules are determined by the sum of the van der Waals radii of the atoms, i.e., by 'contact' interaction with the monitored molecules. Two extreme situations of recognition sites are realized in polysiloxanes and small calixarenes which result from principal differences in their geometric structures. Polysiloxanes consist of a polymeric [RR'Si-O-] 'backbone' and different organic groups R and R' (Table 2). The geometric structure of the simplest polysiloxane with R = R' = C H 3 , i.e., poly(dimethylsiloxane) (PDMS), is well known [9]. At low temperatures, short-range order forces lead to a helical microconformation of the Si-O chain over several atomic distances. However, the geometric structure on a larger scale may more adequately be described with a 'worm-like' model of the individual polymer chains. This takes into consideration I

-Si--o

~

t

I "~IP"',',°~si/

o-si....s~. , o . ~, , ~

s~

(b)

Si~l\

>.~.I

I ~,

(a~ 3 .I

._ .~

I

(a)

-, ,O-si/

0_9--

Si--o ''~' /

"o,

the high torsional flexibility of the Si-O bond which leads to very low glass and melting temperatures ( T ~ = - 1 2 5 °C and Tr, = - 4 0 °C) of PDMS [10]. The geometric structure of the polysiloxane matrix offers a statistical time-dependent distribution of recognition 'sites' for organic molecules. The sites are formed by the short-range ordering of small intercepts of the RR'Si-O chains around an individual solvent molecule. Calixarenes as organic cage compounds consist of several aromatic rings (we chose 4, 6 or 8 rings) condensed with methylene (--CH2-) groups to form macrocycles of different sizes (Table 2). Calix[4]arenes provide a hydrophobic and hydrophilic site and hence form preferentially layer structures in the crystalline state. In the case of the relatively small calix[4]arenes, the geometry of the recognition site does not change significantly upon interaction with guest molecules. Since the 'calyx' of calix[4]arenes has a well-defined but small size and a limited torsional flexibility of the dihedral angle around the methylene groups, these molecules are expected to exhibit a pronounced shape selectivity for different solvent molecules. The larger sizes of calix[6]arenes and calix[8]arenes, in contrast, are expected to form complexes with more than one of the solvent molecules chosen in our study and hence to exhibit less selectivity. This situation may be considered as an in-between situation between the well-defined 'static' structure of recognition sites in calix[4]arenes and the 'fluctuating' structure of recognition sites in polysiloxanes. We use two different theoretical approaches to estimate the selectivities of the two 'model materials', calix[4]arenes and polysiloxanes, for the detection of different solvent molecules. For calix[4]arenes, we compare the selectivities with interaction energies derived from force-field calculations on well-defined molecule/ calix[4]arene complexes. For polysiloxane, interaction energies are derived using a phenomenological thermodynamic approach.

I

"13"Si~

NOOH HOOH

Fig. 2. Interaction mechanisms of organic solvent molecules with poly(dimethylsiloxane) (a) and with t-butyl-calix[4]arene (b).

3.2. Potvsiloxane-based quartz microbalance sensors The bulk dissolution of solvent molecules in polysiloxane layers can be monitored by quartz microbalance sensors. They measure changes Af in the fundamental oscillation frequency fo. To a first approximation, Af results from an increase in the oscillating mass Am. For all the solvents listed in Table 1 and the polysiloxanes listed in Table 2, we found that sensor signals Af are completely reversible. We determine response and decay times in the order of minutes at T= 293 K. For low partial pressures Pi 7,100 Pa, a linear response is found (Am ~Pi).

40

At constant temperatures (263 ~
(1)

with A as coated area and Ce as mass sensitivity. From mc=c,, the sheet concentration cn rnc2cL,NA cm-

(2)

Mc,cL,A

of dissolved C2C14 molecules is determined as particle concentration per unit area. Here, Mc~ct, is the molar gram-weight of C2C14 and NA the Avogadro number. We find co = 0 for an extrapolated thickness d = 0 and hence a negligible surface concentration c(~)=0. Evidently, the interaction of C2C14 molecules with PDMS films leads to a homogeneous bulk dissolution (absorption) in the polymer matrix with negligible surface or interface enrichment (adsorption). The slope of cD =f(d), i.e., the bulk concentration C(b) is identical to values obtained from rnc2caNL

(3)

Mc2cl,, V

C(b)--

with V as volume of the PDMS layer. The amount of bulk dissolution and hence the sensitivity to monitor different solvents is described quantitatively by the partition coefficient fp/g=C(b)/Cg with c as particle (or

T 2.

PDMS/C2CI

4

molar) concentration (here: of C2C14) in the polymeric and gas phase, respectively. For PDMS, PMPS, PCMS and Chirasil-Val the fp/g values are approximately independent of partial pressures at a constant temperature (Henry's law). Even if two gas components are present, the individualfp/g values remain constant in many cases. An example is PDMS exposed to C2C14/n-octane mixtures. Phenomenologically, the dissolution is described in the framework of classical thermodynamics (see Appendix). The molar enthalpy of dissolution AH °, the corresponding Gibbs enthalpy AG ° may be determined from the experimentally determined temperature dependent of the partition coefficient fp/g (Fig. 4). Since AG ° = All °- TAS ° = -RT

-10 E

-4

0

-1-

(4)

and ln(fp/g) = A S ° / R

(5)

AH°/RT

-

holds, the values AH ° (AS °) can be derived from the slope and intercept at T - 1 = 0 of a plot ln(fp/g) versus T -1.

Independently, values AH ° and AS ° and hence the partition coefficient fr,/g can also be estimated for each polysiloxane/solvent system from the values AH ° and AS ° of condensation and from the values AH ° and AS ° of mixing. Results of experimentally determined and calculatedf~/g values obtained for PDMS are shown in Fig. 5. The absolute values of partition coefficients (which correlate with the sensitivities of mass-sensitive sensors) are found to be larger than theoretically expected. This may result from conformation entropy contributions which are not considered in our simple thermodynamic approach. However, a good accordance of the relative values (which correlate with the selectivities) is found for many different solvents.

,s T

T=293 K, Pc,cl =150 Pa

ln(fp/g)

•

T[K] 310

300

I

I

290 I

l

280

270

260

I

I

I

PDMS/C2CI4

0 I

"5

[]

o

Q.

%1 =0

o

,

o.o

.

0.5 d

~

,

8

-

,

o

1.o [10 °4 cm]

P

Fig. 3. Equilibrium values o f frequency changes n f and sheet concentrations cD o f dissolved C2C14 molecules as a function o f thickness d. T h e s e results are obtained from P D M S - c o a t e d quartz microbalance sensors at a constant partial pressure Pc2a~=150 Pa and t e m p e r a t u r e T = 2 9 3 K. C(b) and c(o d e n o t e bulk and surface concentrations, respectively.

~ > ~[m{In(f p,g)}= ASs°/R IT' 7 I

I

I

I

3.2

3.4

3.6

3.8

10 3 T -~ [K -1] Fig. 4. Partition coefficient fp/g o f C,2C14 in P D M S as a function of t e m p e r a t u r e T in ln0~p/~)-T -1 plot.

41

T'=298 K n-octane

\

T 8-

%

n-BuNH 2 %/"j. CCI, " /

n-hexane (i-Pr),O ~ /

6"

4" n-hexane

(i-Pr)20 \ C H C I , ~ 2

~

~C2Ci' e\ Me-$ - " Me-C,, . . . . . . . . . .

n-BuNH2 / i-' ".~.~..I~ ~ -A~. CCl4

" \ . . . . Me-* .> Me-, Me-C,H.

I 1.3

I 1,4

I 1.2

(b)

- "

1.5

T b/T' Fig. 5. Ln(fr~g) as a function of reduced boiling temperature Tb/ T' for different solvent molecules in PDMS: (a) calculated values; (b) experimental values for T'= 298 K. Response

of sensor 1 (PDMS)

experimental setup which produces fast and rectangularshaped partial pressure variations, an unequivocal determination of sensor signals (such as the maximum temperature change) is possible (Fig. 7). For the PDMS/ C2C14 system as a typical example, a correlation is found between the maximum positive temperature changes ATmaxand Pc~ca during a constant absorption 'bath' temperature of the outer thermopiles. The response times tmax t o reach ATm~ depend only on the diffusion coefficients of the solvent molecules. One great advantage of this sensor principle is the perfectly constant base line as a reference which is always obtained after gas specific rise times ~1 (see Fig. 7). 3.4. Polysiloxane-based capacitance sensors As shown in Fig. 8, capacitance changes AC determined with interdigital electrode devices contain contributions from changes in the relative dielectric coefficient e2 of the polymer and/or from changes in the effective thickness d of the polymeric film [7]. The

u-octane

I 400PDNS/C2Ck 20

Af

507

T=293K 111

Pc2ck/Pa

172

227

2816

. perchloeoethylene

""/!!"..

,tot~1271---

>

200

4O

r?, O

^,

~,,~ ~

~rajf.. _

~f

2-

Response

"

~

~

':

of sensor2

...'

~

- oo

Response of sensor 3 (Chirasil-Val)

-80

;

2o3o

obo t/s

(a)

>

fPDMS/C2CkT=293K

4OO

200]

\

Pc~ck=2816 Po

T e m p e r a t u r e c h a n g e s during dissolution o f solvent m o l e c u l e s in p o l y s i l o x a n e s are utilized in calorimetric sensors. H o w e v e r , s i n c e A H = 0 h o l d s u n d e r e q u i l i b r i u m conditions ( n o t e the difference b e t w e e n A H and AH°), A T effects are only m o n i t o r e d during pressure variations u n d e r c h o p p e d flow conditions. W i t h an

6doo

-8o t "~Tmax

0

-200-

i 8001

.40

t~x

,y, ¢2 0

•-40

-80

-400.

3.3. Polysiloxane-based calorimetric sensors

I-<3

-40

- L0o

l To recognize different solvent molecules in a mixture with high accuracy, PDMS-, PCMS- and Chirasil-Valcoated quartz microbalance sensors may be utilized in simple sensor arrays. The principle is demonstrated in Fig. 6 [11]. Since the different partition coefficients are to a good approximation independent of the partial pressures, the direction of the three-dimensional vector is specific for the specific individual solvent or solvent mixture.

0"

>

(PCMS)

Fig. 6. Three-dimensional plot of sensor responses At"(in arbitrary units) of PDMS-, PCMS- and Chirasil-Val-coated quartz microbalance sensors for different solvents.

0

7~0 (b)

t/s

Fig. 7. Typical responses Vme~mo~AT of the thermocouples of our calorimetric thermopile sensors coated with PDMS as a function of time for stepwise exposures to different partial pressures of C2C14 in air: (a) overview; (b) details for one specific absorption cycle with response time 71 and decay time r2. Vtherrno is the signal of three thermopiles connected in series.

42

~- ~ u n i t

cell

•/

~electricalfield AC" AE~, ~ S ~electrode C-I~C'c3 : f' - ~ " i~ ' f ' /l ~ - ~m' ~ ' ~ "s/ S ~ ypm l°er

t

-40

Fig. 8. Schematic representation o f a 'unit cell' of polymer-coated interdigital structures with the t h r e e permittivities e~, e2 and e3.

60 d

-80

30

61

I l I

I

Q- 51.0

-

f

-

=

-

0

Fig. 9. Typical responses AC of capacitance sensors coated with PCMS as a function o f time for stepwise exposures to different partial pressures o f n-hexane in air.

B u

0 latter results from a temperature- and partial pressuredependent swelling of the polymer film. This swelling can be made use of to design optical sensors for the determination of solvent molecules in the gas and liquid phase [6, 12]. Since M effects are not monitored sensitively by capacitance measurements, polysiloxanes must be used which show high values of e2. An example is PCMS with e2 = 10 which makes it possible to detect even nonpolar compounds like n-hexane (Fig. 9). 3.5. Calixarene-based quartz microbalance sensors

Specific 'key-lock' interactions between calix[4]arenes and solvent molecules were monitored with quartz microbalance sensors. Typical results obtained for different thicknesses 6 ~
6'o t [min]

i-P r o p y l - c o l i x [ ~ l o r e n e PC2ClC200 PO J T=298K

5

obo t[s]

•t00 1

Fig. 10. Typical responses Af of quartz microbalance sensors coated with different thicknesses d o f i-propyl-calix[4]arenes as a function o f time after exposure with Pc2o4 = 200 P a in air at T = 2 9 8 K.

(.9

500505"

~

I ;

122

50

i

L

11/,

PC6H~IPa I

--

[nm

PCMS/n-hexane T=293K

o

f

30

5151

200Po

T=2~K

t~

520

I~cI~_=

i-Propyl-calix[L]arene

(6)

'~C(s) 0 ....

sb . . . . d [nm]

~6o ' ,-

Fig. 11. Sheet concentration cD of C2C14 molecules (molecules/ cm 2) in i-propyl-calix[4]arene as a function of thickness d at Pc~cu = 200 Pa and T = 298 K.

is obtained at constant partial pressures and temperatures with a typical result shown in Fig. 11. Bulk and surface concentrations c(b) and c(o, respectively, of C2C14 molecules are determined from the slope and intercept in this Figure. We find the value c(s) to be larger than the layer concentration in the bulk as calculated from c2/3 (b)- This effect indicates the favoured accessibility of calixarenes at surface sites if compared with bulk sites. However, at larger thicknesses the overall sensor signal is mainly determined by the bulk since the number of bulk sites increases linearly with film thickness. The response times, however, become larger (see Fig. 10). In order to estimate activation energies of desorption from surface sites of C2C14 molecules, we performed thermal desorption spectroscopy on in situ prepared calix[4]arene films [13]. The low adsorption temperature (Tad~= 120 K) leads to an adsorption of C2C14 molecules only at surface sites. We determined Ed = 50 kJ/mol. In addition, we determined the binding energies of organic molecules in the calixarene macrocycles in forcefield calculations by using the TRIPOS program as a part of the SYBYL software package [14]. The total energy E t o t of the calixarene/molecule complex is given by the sum over the bond stretching energy

43 , 9.0'

T

t-Butyl-calix[4]arene T=298

K, Pi =200Pa

CHCI:,~ JA ~ " ~ C=CI,

8.5' ¢-

b

8.0

e

n

~

I

55

60

65

Eb[kJ/mole] Fig. 12. Logarithm of partition coefficients fp/g as a function of binding energies Eb of different solvents 'i' in t-butyl-calix[4]arene. Estr, the angle bending energy Ebb,d, the out-of-plane bending energy Eoop, the torsional energy Etor, the van

der Waals energy Evdw and the electrostatic energy Ee~e: Eto t = ~ E s t r 4- ~Ebend 4- ~Eoop 4- ~Etor 4- ~Evdw 4- EEe~e

(7) For the estimation of electrostatic energies, we determined the partial charges at the atomic positions in a semiempiric approach by using the PM3 program of the MOPAC package. As an example, we first compared the calculated geometric structure of the inclusion complex of pyridine in crown-bridged t-butyl-calix[4]arene with the crystal structure data given by Andreeti et al. [15]. The deviations of the theoretically determined atom positions from these data are smaller than 5%. We then determined binding energies Eb between calix[4]arenes and different solvent molecules. They are given by the difference of the total energy of the 'empty' calix[4]arene and the calix[4]arene/solvent supramolecular unit at the minimum of E,o,. We find a correlation between theoretical binding energies from force-field calculations and the experimental partition coefficients fp/g (Fig. 12). The latter values were determined from the experimental bulk concentrations C(b) (compare Fig. 11). The partition coefficients fp/~ are given by the Gibbs enthalpy AG ° with its enthalpy and entropy contributions AH ° and AS ° (compare eqns. (4) and (5), which can also be applied here). The link between these values and the calculated energies El (compare eqn. (7)) before and after interaction is given by statistical thermodynamics [8]. This would, however, require additional information about all energy states of calix[4]arenes and molecules before and after interaction.

4. Conclusions We have studied two different model systems to prepare sensitive and selective layers of chemical sensors

which may be used to detect organic solvent molecules in air. These sensors are based on changes of mass, temperature, thickness and capacitance which occur during interaction with the solvent molecules. Pronounced differences exist between the structures of recognition sites in the two model systems, i.e., calix[4]arenes and polysiloxanes, which range from welldefined time-independent geometries to fluctuating time-dependent geometries. Both recognition sites are more complex than recognition sites on inorganic solid surfaces usually used in chemisorption sensors (e.g. point defects on oxide surfaces which act as chemisorption sites and which are well understood [16]) but have by far simpler structures than recognition sites of, e.g., antigene molecules in biosensors which are not understood at all at the detailed molecular level. We find that selectivities of polysiloxanes can be understood in a simple thermodynamic description of the bulk dissolution of the organic molecules. Selectivities of calixarenes can be understood by calculating binding energies in force-field theories.

References 1 W. G6pel and K.D. Schierbaum, in W. G6pel, J. Hesse and J.N. Zemel (eds.), Sensors: A Comprehensive Survey, Vol. II, Part 1, VCH Publishers, Weinheim, 1991, pp. 1-27. 2 J.W. Grate and M.H. Abraham, Sensors and Actuators 13, 3 (1991) 85-111. 3 F.L. Dickert, A Haunschild, P. Hoffmann and G. Mages, Sensors and Actuators B, 6 (1992) 25-28. 4 M.S. Niewenheuzen and A. Venema, Mass-sensitive devices, in W. G6pel, J. Hesse and J.N. Zemel (eds.), Sensors: A Comprehensive Survey, Vol. II, Part 1, V C H Publishers, Weinheim, 1991, pp. 648-680. 5 K.D. Schierbaum, A. Gerlach, M. Haug and W. G6pel, Sensors and Actuators A, 31 (1992) 130-137. 6 W. Nahm and G. Gauglitz, G I T Fachz. Lab., 7 (1990) 889. 7 M. Haug, K.D. Schierbaum, H.E. Endres, S. Drost and W. G6pel, Sensors and Actuators A, 32 (1992) 326-332. 8 Compare, e.g., P.W. Atkins, Physical Chemistry, Oxford University Press, London, 1986. 9 M.G.Voronkow, V.P. Mileshkevich and Yu. A. Yuzhelevskii, The Siloxane Bond, Consultants Bureau, New York, 1978, p. 50. 10 J.E. Mark, in J.M. Zeigler and F.W. Gordon Fearon (eds.), Silicon-based Polymer Science, The American Chemical Society, Washington, DC, 1990, pp. 47-68. 11 Compare, e.g., K.D. Schierbaum, U. Weimar and W. G6pel, Sensors and Actuators B, 2 (1990) 71-78. 12 M. Haug, K.D. Schierbaum, G. Gauglitz and W. GOpel, Sensors and Actuators B, 11 (1993) 383-391. 13 K.D. Schierbaum, A. Gerlach, W. G6pel, MOiler, F. VOgtle, A. Dominik and H.J. Roth, manuscript in preparation. 14 A. Dominik, Diploma Thesis, University of Tiibingen, 1993. 15 G.D. Andreeti, O. Ori, F. Ugozzoli, C. Alfieri, A. Pochini and R. Ungaro, J. Inclusion Phenom., 6 (1988) 523. 16 W. G6pel and K.D. Schierbaum, in W. GOpet, J. Hesse and J.N. Zemel (eds.), Sensors: A Comprehensive Survey, Vol. II, Part 1, VCH Publishers, Weinheim, 1991, pp. 120-157.

44

Appendix Thermodynamic treatment of sensor sensitivites and selectivities The Am effects upon exposure of one specific solvent 'i' can be understood in the framework of classical equilibrium thermodynamics if equilibrium bulk concentrations of the molecules 'i' are adjusted in the polysiloxane layers at constant partial pressures p and constant temperature T. Under these conditions, the chemical potentials of the molecules in the gas phase (/z~) and the polysiloxane (/zp) are identical: p.g =/zp

(A-l)

The chemical potential #g can be split into a temperature-dependent standard chemical potential/z~* at a constant standard pressure p* and a term R T In(p/p*). Alternatively, we may express/zg by particle or molar concentrations Q in the gas phase (in units m -3 or mol/m 3) and introduce a temperature-dependent standard chemical potential /~g at a constant concentration c~ and a term R T ln(Q/c~): I,~ = Iz~* + R T In(p/p*) = t ~ + R T ln(cg/c~)

(A-2)

Here, we assume ideal gas behaviour at low partial pressures with C s = P / R ' T ( R ' = 8.2056 Pa/(m 3 K mol)). Correspondingly, we introduce /zp by

with AG ° identical to the negative value of the Gibbs enthalpy of evaporation AG °. The standard Gibbs enthalpy of mixing AG° may be estimated according to the Flory-Huggins theory [A-l] in a simple lattice model simulating the polysiloxane matrix: AG ° =RT~i(1 - qb~)X - T[-R4)i ln4)~-P- ~R(1- ~ ) ln(1 - 4,)] = A H mO - T A S °

(A-6)

with ¢i = V d V as the volume fraction of the solvent molecules in the total volume V, X as Flory-Huggins parameter and P as degree of polymerization*. For the volume fraction, qbi=C(b)~31 holds (with ~3i as concentration-dependent partial molar volume of the solvent in the polysiloxane matrix which may be approximated by the concentration-independent molar volume of the solvent vl). The latter is given by pi/Mi with pi as density and M~ as gram-molecular weight. In the framework of the simple lattice model of the condensed solvent phase and the polymeric phase, the Flory-Huggins parameter X describes changes of enthalpy AH°m in terms of changed contact interaction energies u,, upp and u~p between solvent molecules 'i' and the monomer units of the polymeric chain 'p': )(=z[Uip

-

0.5(u,

up,)]/kT

-

(A-7)

The value of X can be calculated from the Hildebrand parameters 6i(p):

(A-3)

Izp = I~, + R T ln(ce,)/c~t,))

X = vi/RT(8, - 6o)2

with C(b) as particle or molar concentration C(b) in the bulk and ~ as the standard chemical potential at concentration C~'b). The enrichment of solvent molecules in the sensitive coating with respect to the gas phase is described by a temperature-dependent equilibrium constant denoted as partition coefficient fp/~=c(b)/Q if C~=C~,= 1 mol/m 3 are chosen as standard concentrations. Then [/Zg-/z °] = - R T In C(b) = - R T ln(fp/s)

(A-4)

Cg

holds. The difference [/z~-/zg] corresponds to the changes in the standard Gibbs enthalpy AG ° (here and in the following, molar quantities are considered only) during the dissolution of molecules 'i' in the polymeric matrix. Formally, AG ° may be split into the standard Gibbs enthalpy of condensation AG ° = [/~o_/.%], mixing AGm-[/Xp-/Xc] and volume expansion AG~v o

__

0

O.

o

AG°=AG°+AG°+G°,

= -AG°+AG°

+G¢°I

(A-5)

(A-8)

of the solvent 'i' (see Table 1) and the polymer 'p'. The Hildebrand parameter is defined as square root of the density of cohesion energy: o

~i(p) [A Ue,i(p)/Ui(p)] •

(A-9)

1/2

.

O

O

.

Here, the approximation AUe,~0)= AHe.i0) is used. Values 8p of the polymers are usually derived from the density of cohesion energy of corresponding oligomeric compounds with similar structure to the polymers. As a typical example for a quantitative evaluation, Table 1 summarizes calculated values of the Hildebrand parameters ~ for the different solvents used in this study and calculated values of the Flory-Huggins pa*The degree of polymerization is defined as P= (Mp-Mc)/Mu with Mp, Me and Mu as gram-molecular weights of the polymer, t h e terminal groups and the monomer. In this approach, P is approximated by the ratio of mole volumes of the polymer and the solvent. This requires identical volumes of solvent molecules and the monomeric unit.

45 rameter X for PDMS/solvent combinations with 6p = 7.5 [A-l]. For X<0.5 we expect a dissolution of solvents. We calculate A G ° ~ I kJ/mol for volume fractions q~i~0.2 which are small compared to the AG ° values (compare Table 1). Differences in experimentally determined and calculated values AG ° are therefore at-

tributed to the volume expansion (swelling) of the polysiloxane films.

Reference

A-1 H.-G. Elias, Makromoleki~le,Vol. I, Hfithig & Wepf Verlag, Basle, 1990, p. 663.