Eur. fo/vn. J. V ol.

Pergamon

31, N o. 7. p. 614,09-

195

Copyright (‘ 1995 Elsevier Science Ltd in Great n .iaB rt lA rights reserved 0014-305719s $9.50 + 0.00

dentP ri

GAS CHROMATOGRAPHIC MEASUREMENTS OF SOLUTE DIFFUSION IN BLENDS OF PHENOXY AND POLY( 1,4-BUTYLENE ADIPATE) C. URIARTE, npeom D atr

de neC aic

J. ALFAGEME,

y ncoT eag il doA aprt

A. ETXEBERRIA

de o,em ilP sr , 2 7 0 1 8 0 2

da& tF c nS a nai,tSbsea

de ,acim Q u

and J. J. IRUIN dsvU nirae

1de

siP a

ocs,V a

niS pa

(Receiaed 6 June 1994; accepted in ,$nal form 30 August 1994)

etn if niu o tld fuo nids snoeictf f ndao-tce o ni ypol oxyhdr( hter of snobilphe A , oxy)P n,he ypol ney lb t( u dap,eit B A )P nda a 5 : 50 ndebl 0 ew r desuit ungis serniv gsa hog-tacm r pahyr C )E (. snem tuM ar ew r dem rpf o ta enftd ir easpm rut boave hte lahm tre rnoiats of hte ysroanit p.shea A ndeb l fuo nids noeictf w o elr nhta hta edtcipr by hte nirlae cihm roltga ngxim rule was observed. The experimental results were analyzed using free volume and activated state theory concepts. Experimental data at zero flow rate were used ni hte uonictal of hte erf negyr dytines B. h cw i ocusnat rf hte ey o m l-r o p aco nietr ni hte nd.ebl Abstract-The

limits the precision of measurements at conditions approaching infinite dilution of the solute and for systems where the diffusion coefficient is strongly concentration dependent. Inverse gas chromatography (IGC) is a technique that can circumvent some of the problems attendant to gravimetric sorption experiments [3]. Transport limitations in the stationary phase can produce significant broadening and distortion of the chromatographic peak. This phenomenon can be exploited as a way of measuring the diffusion coefficient of the probe substance in the stationary phase. For packed columns, diffusion coefficients are determined from an analysis of the variation of the plate height H with the average carrier gas flow rate u, by the use of the van Deemter [4] equation

O R ID N U T C

The transport of permeant molecules into and through polymer films depends intimately both on the diffusion and sorption properties of the solute on the polymeric material. Graham [l] recognized that the overall transport processes involved the solution of a gas at one surface followed by its diffusion through the film and subsequent evaporation of the diffusing species from the downstream film surface. Most of the published research prior to 1950 was primarily concerned with diffusion in rubbery polymers. Small deviations from the single mechanism described above are encountered for rubbery systems containing crystalline regions that are susceptible to reordering by an interacting or plasticizing vapor or liquid penetrant [2]. In general, vapors and liquids do not obey Henry’s law even in rubbery polymers. Furthermore, the diffusion coefficients are often highly dependent upon the concentration of the penetrant in the polymer. The dependence of the diffusion coefficient on sorbed penetrant concentration, for systems in which solubility essentially follows Henry’s law, has usually been empirically represented by equations of the form

H=A+B/u+Cu

where A, B and C are constants and the plate height H is determined from the width of the eluted solvent peak. The constant C in equation (2) accounts for mass transfer in the stationary polymer phase and is related to the diffusion coefficient D as follows C = @/n’)(d;/D)[k/(l

D = D,exp(yc)

(2)

(1)

+k)‘]

(3)

where dr is the thickness of the stationary phase, D is the diffusion coefficient of the vapor in the stationary phase, and k is the partition ratio expressed by k = (t, - t,)/r,, where t, is the retention time from the injection for the vapor, and t, is the time for the carrier gas to pass through the column. The above methodology implies that all mass transfer resistance is due to diffusion in the stationary phase and the stationary phase is uniformly distributed on the surface of a uniform spherical packaging. However, there are other processes which can influence peak shape [5]. Some of the more significant include axial gas-phase dispersion, channeling of the

where y is a characteristic parameter of the system at the given temperature, and D,, is the diffusion coefficient in the limit as c 4 0. This type of equation is generally only applicable to systems where the concentration of sorbed vapor is small or the temperature sufficiently high such that Henry’s law is a reasonable approximation. Conventionally, diffusion coefficients for solutes in molten polymers are determined by gravimetric sorption/desorption experiments. In this type of experimental technique, the necessity of high solute concentration to produce measurable weight changes 9 0 6

carrier gas, back-mixing in the injector and detector. nonuniform injection of sample. gas-phase masstransfer resistance, surface adsorption effects, and nonlinearity of the absorption isotherm. The other factors must either be suppressed in the experuncnt~ [6] or accounted for in the model used to analyre the data. One important condition is that the amount of vapor injected should be as small as possible: at infinite dilution the partition isotherms ma! approach linearity, and the simple model assumed m the Van Deemter equation may bc adequate Despite these advantages and despite the ~tdcspread use of IGC for thermodynamic measurements. there have been relatively few applications to the study of polymer solvent diffusion. The fir\1 reported use was by Gray and Guillet [6]. wht~ stud14 the diffusion of benzene. decane and d~~iecanc 111 polyethylene and natural rubber. They wcrc un:tble to prepare suitable columns with natural rubber but did reasonable diffusion coethcicntz \cith obtain polyethylene. Braun et rrl. 171 measured ditfustor! coefficients for decane. tetralin, dccalin and tuc commercial plasticizers in po!ycthylcne Haukct (‘i ~1 18, 91 have studied the dtffusion of alkanc\ III 7’;1it ;lnd 4hu\hihad;l / 10; dimethylsilane polymers used the method to study the dilfusiun t>l’ drlfc~-cn organic solvents in PVC. PS and PMMA. Scr11cl11I I: measured the diffusion cocflicicnt of octadecanc II‘ high-density polyethylene. Pawlisch (‘1 ir/ [ 121IMLC studied the diffusion of solutes in thin. uniform polymer films coated on gl;tss cap~llal-1 columns In some of these paper\ the uncct-tamt; ot’ th determination factor of the geometric I;IC~I)I i (expressed as 8:~‘) in equation (3) haz beer1 NIIsidered. In fact. Hu (11crl. [ 111have argued that ICX cannot provide absolute ~alucz of tiiffu\ton CI~ efficients unless one determInes the numerical \ aluc 01 y by comparing the values of diffusion coeflicicnt~ obtained by IGC with those dctcrmincd hi other independent methods. such as the \orptmn method Using glass beads as support. PS :md PV,4 ;I\; pal!met-s and benzene, ethyl henzenc. toluenc and n-dccane as solutes. they obtained ;t r, L;IIW (-II‘I (1 much lower than 8 rrc’ or 2 3 proposcti 1~) Hawks\ [IJi Different papers have been puhhshctl ;IIX~UI g‘r‘ transport properties of miscible bends [IS 241. PoI! mer-polymer interactions can strongly tntlucncc the gas sorption and transport proper-tic\ 01‘ the hIend\. mcaSut-t’Conversely. gas sorption an d transport ments can be used to study polymer-polymer Intel-actions. Various types of behavior arc possihlc. depending on the strength of thcsc in~c~-;~ct~~rl~ In recent papers [25-271 we have usud IGC ‘12r~U:~J of calculating polymer-polymer interaction cncrg! densities (B) in miscible blends ofpoly(hydroxy ethcrof bisphenol A). The present paper is a preliminary

Length (m) II

I2 12

test of the extension of IGC measurements of infinite dilution diffusion coefficients in such types of polymer blends EXPERIMENTAL

Phenoxy resin (PH) was obtained from Quimidroga (Barcelona, Spain) and corresponds to the PKHH product nf Llmon Carbide. The commercial sample was purified by

\oiutton

m dioxane and precipitation

in methanol.

Its

weight distribution, measured by GPC in THF (Waters ALC 150 Gel Permeation Chromatograph) at 303 K gave an M, = 18,000 with a polydispersity ‘II, \I - 2.x [ZS]. Poi! ( i.4-butylene adipate, PBA) was obtained from 4idrrch Chemical Co. (cataloaue No. 18,150-l). Its intrinsic : r>cosrty in benzene at 298 K was 0.322 dl/g. n-Octadecane (chromatographic quality) was used as a drffusant probe. In order to reduce bulk sorption into the polymer and not contribute to the retention of the adsorbate
I tri%p,rc chromatographic measurements were carried out rr: .I Perkrn Elmer SIGMA 300 gas chromatograph ~~~lurpped wrth a flame ionization detector and connected to ,,,I Olivetti M-24 personal computer with appropriate soft\\:rre in order to yield high-precision retention data. Nitro~cn was used as the carrier gas and methane as a nonrntcracting marker. Pressures at the inlet and outlet of rhc column. read from a mercury manometer were used to , rrmpu~e corrected retention times by the usual procedures IV The columns were prepared in the usual manner [29] using $rar beads ho:80 mesh as packing support. The pure polymers and the polymer blend were coated from a THF \olutron onto the packing support. After drying in a vacuum .~\c‘n for w 4X h at 323 K, the coated support was packed Into a I linch o.d. stainless steel column by applying ~l~cuunr to the end. Glass wool was used to block the ends 01 the columns. The weight and percentage of the stationary pha\c were determined by immediate weighting. The relative ~~oncentration of the polymer in the blend was assumed to he rdsntrcal to that in the solution prior to the deposition on rhe Inert support. A description of the columns is given in fable I The oven temperature was measured within *O.l in the u hole temperature range. The molecular probe, including a mall amount of methane marker (nditioned at temperatures above r, or TM for CLI48 hr prnor lo use, while N, was flushed through the column in order that it should come to equilibrium. The average linear Row rate at the column temperature tcorrecled for gas compressibility) was determined using the relatronship [5]

Pa&UIg ,“ppM

WeIghi 01 pachmg lli coIumll I@)

Polymer coating

Weight of coating in column (g)

Gla\a bead> 60:X0 mesh Glassbead\ 60.80 me\h Glass bead\ ho:80 mah

43 495

Phenoxy

0.130

43 10-t

PBA

0.140

41 Fib!

PH’PBA (50: SO)

0.142

Gas chromatographic

measurements

611

-20.0

-22.0 z

1.0

2.0

3.0

4.0

5.0

6.0

u(cm/s)

7.0

6.0

(4)

where j = (~PMPJP,)~

- l)i((~,lp,)3 - 1)

(5)

p,/p, was the ratio of column inlet pressure to column outlet pressure, Cwas the column length and f, is the retention time of the noninteracting marker. If H was an apparent plate height for the column and conditions, then H = (L/5.54) (d/r,)’

(6)

where t, was the indicated retention time from injection to the peak maximum and d was the measured peak width at half height in the same units as t,. A minimum of three measurements were taken for each flow rate and temperature, and an average plate height was calculated. The average thickness of the polymer layer d, was taken to be dr = (QP,)(~

V/r)

where wp and pp are the weight and density of the polymer coated, V the volume of all the glass beads introduced into the column and r an average radius. The value of r was obtained from measurements of bead diameter in an optical microscope and V was measured volumetrically. The density of the phenoxy resin was obtained from [30] I/p = 0.8362 + 3.92. 1O-4(T - 273.2) + 4.84. IO-‘(T - 273.2)’ and the density for the poly (1,Cbutylene adipate) (PBA) was obtained from a group contribution method [31], its value being taken as 1.042 g/cm3 within our temperature range.

Table 2. Diffusion Polvmer

coefficients

Temperature C K)

for n-octadecane D (cm*/sec). IO’

Phenoxy

418 423 428 433

0.02724 0.04052 0.05398 0.11909

PBA

403 408 413 418

0.03679 0.04378 0.04938 0.05508

PHjPBA (50 : 50)

403 408 413 418

0.00214 0.00246 0.00302 0.00372

-

-24.0

-

2.30

Fig. 1. Van Deemter curves for the columns: (0) Phenoxyn-octadecane at 423 K; (A) PBA-n-octadecane at 418 K; (0) Phenoxy/PBA(SO: 50)-n-octadecane at 418 K. u = jfjt,

-23.0

1O-3

2.35

10s3

2.40

lo- 3 2.45 lfrw-')

1O-3

2.50

10e3

Fig. 2. Arrhenius plots of diffusion for (0) Phenoxy-noctadecane; (0) PBA-n-octadecane; (A) Phenoxy/ PBA(50: SO)-n-octadecane. RESULTS

AND DISCUSSION

The results of a series of experiments to measure the solute plate heights from the eluted peaks as a function of flow rate are shown in Fig. 1. When sufficiently slow flow rates are employed, the plate heights usually pass through a minimum, as predicted by Van Deemter equation (2). In our data, this can be seen in the blend case. At higher flow rates, H increases linearly with U. On the other hand, high plate heights may be rationalized by considering the nature of the polymer. The rate of diffusion through the blend is much slower than through the pure components, and the smaller value for the diffusion coefficient results in a larger C term in the Van Deemter equation (2). The slopes of lines relating plate height to corrected linear flow rate were used to obtain the C term. A requirement for interpretation of the C term is that the geometry of the stationary phase should be well defined, so that a meaningful estimate of the thickness dr of the polymeric phase may be obtained. This appears to rule out columns coated on chromosorb or other diatomaceous earth supports which have a very complex structure [32]. Hawkes c’t al. [33] suggested that glass bead columns with a liquid phase attached to bead contact points by capillary forces provided a better defined liquid phase distribution, If it is assumed that a polymer coating on glass beads exists as a film of mean square thickness df, then D may be obtained from the Van Deemter C term [6]. Although it is impossible to test the uniformity of the polymer coating around each particle or from particle to particle, the use of a very low coating tries to ensure a rapid equilibrium between the polymeric stationary phase and the penetrant. An average thickness was calculated from the amount of polymer and the geometric area of the bead surfaces, and D was thus obtained at different temperatures, as can be seen in Table 2. There is a great inherent uncertainty in the thickness of the polymer layer. A f 10% uncertainty in the area of the beads will lead to *20% uncertainty in D, and further errors will result from nonuniform layer thickness and geometry. Furthermore, in this technique, the thickness enters as a squared term in the calculation of the diffusion coefficient.

C. Uriarte er a/

612

These diffusion coefficients for n-octadecane in the pure polymers and in the blend at different temperatures can be presented as Arrhenius plots in Fig. 2. Despite the data obtained well above the glass transition or melting temperatures, they did not give linear Arrhenius plots. This is particularly evident in the case of the phenoxy resin. Similar behaviors have been observed in other cases [6, 131. Although Gray and Guillet [6] attributed this nonlinear relation to crystallinity changes with temperature in the case of their poly(ethylene) samples. Hu cl (11. [13] have explained this type of behavior on the basis of the Vrentas-Duda free volume theory. Given the experimental difficulties encountered in extending the temperature range here considered, we were not able to apply this model to our experimental data. Values of the blend diffusion coefficients lie far below those predicted by a linear logarithmic mixing rule In fI = @AIn D, -t (PHIn fZ$.

(8)

This deviation can be qualitatively explained on the basis of the Cohen-Turnbull free volume theory. with similar arguments to those employed by Li (I[ ul. [34] in explaining transport properties of blends of PMMA and PSAN. The diffusion coefficient of gases through a polymer membrane can be expressed as n = A exp( -J.*‘/.,)

(9

where A is a characteristic constant of the gas, /.* the critical free volume required for a jump and t’, the free volume of the polymer. An expression of the free volume in the blend can be written as “ti,i = cb,,~‘i,,+ (/)Lj[‘II++ Al.,

t IO)

of the free volumes of the components A and B and an excess free volume Al.,. Combining equations (9) and (IO) yields the following mixing rule in function

In D - &,&In /I, - &In

D,,=-- L* -- (&&,(r,, “I,,,(‘I.\“111

- I’,~)- + A~.,(q$~,r,.,+ (/I~I.,~~ )I

This blend exhibits other characteristics indicative of exothermic interactions between the components, such as a PBA melting point depression [37]. Those interactions are probably the result of hydrogen bond formation between the hydroxyl group of Phenoxy and the carbonyl of the polyester, similar in magnitude to those reported in blends of phenoxy and poly(c -caprolactone). Sorption measurements above the melting point have also been carried out [38]. The obtained results suggest that the Phenoxy/PBA interaction parameter is negative, a characteristic feature of miscible systems. We can confirm these results using our own IGC data at the lowest flow rate used in the experimental measurements. From retention times it is possible to calculate the specific retention volume Vi, following the well-established data reduction procedure [39]. At 418 K the specific retention volumes in c.c.(g were 327.8 (PH), 668.7 (PBA) and 434.5 (blend). From the specific retention volumes, a rule of mixtures in blends of components A and B can be dcvelopcd from the Flory-Huggins theory for ternary systems [35]

(Ii)

for the diffusion coefficient of a gas In :I polymcl blend of A and B. Since r$,$,(c,, - z),~)’ and J.* ‘(I‘,,,,~‘,,~(‘,~ ) arc always positive, (In D - 4A In D,& - (PI, In D,) is positive if AL-,->,0. Even when AZ’,is negative. the deviation still can be positive if 4A#U(r,, - l’,,, )’ is larger than the absolute value of Ac,(@,(‘,, + &t.IH). If, as in our case. In D < $i\ In D,, - &, In D, then Ar, < 0 and 4A &(crq - Q~ )’ i I Arl.(SAqA + &rn,) I. Negative excess volumes are quite common Iti miscible polymer blends. Although this type of behavior has been associated with specific interactions between the components of the mixture, negative excess volumes have been reported either in hydrogen-bonded polymer mixtures, such as phenoxy/poly(ethylene oxide) [35], or in others with lower levels of interactions such as PS/poly(ochlorostyrene) [36]. Phenoxy/poly(butylene adipate) has been reported as a miscible blend. The existence of a single rB in the Phenoxy/PBA blend, reported in the literature [37] and confirmed in our laboratory. which varies smoothly with blend composition, indicates that Phenoxy/PBA blends are clearly miscible.

where the composition is expressed either by the weight fractions o, or the volume fractions 4,. and B i\ the so-called interaction energy density (in cal c.c.). V is the molar volume of the penetrant and ths term BURT is similar to the Flory-Huggins Interaction parameter. With the specific retention volumes above mentioned an interaction energy density of -4.6 Jx.c. can be calculated for a 50;50 PH/PBA mixture by weight. This result. although negative. is significantly lower than that of - 15.5 J/cc. obtained at 334 K by Harris (‘I trl. 1371by melting point depression measurements. The same authors [38] have also reported a value of 10.Y J:c.c. at 353 K. measured by sorption experiments monitored by using a vibrating piezoelectric crystal as microbalance. At a first sight, it could be argued that these differences could arise from the different experimental temperatures. But, this argument is inconsistent with recent simulations of our group using the so-called Painter and Coleman 90

94

320.0

340.0

360.0

380.0

400.0

420.0

440.0

T (K) F-ig. 3. Simulation of the interaction energy density variation with the temperature for the Phenoxy/PBA (SO:SO) blend.

Gas chromatographic measurements association model [4O] which reproduces reasonably well other properties of blends of phenoxy with the family of aliphatic polyesters. The above-mentioned model allows us to calculate the free energy of mixing at different concentrations and temperatures. These calculations lead us to other thermodynamic magnitudes using classical thermodynamics formulae. The model supposes that miscibility in polymer blends is mainly due to the existence of specific interactions which can be included as a third term in the expression of the free energy of mixing (in J/mol) A% = W(~,lr,)ln

4I + (Mz)ln

+ RT~%$, $2 +

AGH

&I (13)

The first term is the combinatorial free energy of mixing, ri being the number of segments, the second one is only due to dispersive forces and may be calculated from solubility parameters and the third one can be determined from association constants and enthalpies of association which, for a given polymer blend, can be calculated from FTIR measurements on the blends or on mixtures of analog compounds of low molecular weight. The last two terms can be rolled into an overall B term. Constants and enthalpies for mixtures of Phenoxy and linear polyesters have been recently reported by Coleman and coworkers [41]. If we introduce these data in the available association model software [40], it simulates an interaction energy density which varies with the temperature in a slightly parabolic form (Fig. 3), with a value for a 50: 50 blend around - 10.5 J/c.c. The lower B value obtained by IGC can be a consequence of the preferential sorption of the probe between the components of the mixture. Although, in theory, IGC is well suited for the study of mixed polymer systems, in practice it is found that the interaction energy density for a fair of stationary phase components is not uniquely defined for a given composition and temperature. Rather it varies with the selection of the probe, thereby creating a dilemma that is yet to be resolved fully. Conceptually, such variations should not be entirely surprising. Unless the probe partitions randomly between the components of the polymeric mixture, some perturbations in the energy at polymer-polymer contacts should be expected. Our view is that we are measuring a lower B value because the probe is “seeing” a blend composition which is different to that originally prepared. Differences arising from other technical problems inherent to melting point depression experiments or sorption experiments could also be in the origin of such discrepancies. The transport of small molecules in polymers is often discussed in terms of an activated process of the Arrhenius type D = D,

exp(- E,/RT)

(14)

where T is the absolute temperature, ED is the activation energy for diffusion, and D, is a preexponential factor. Based on the found correlation between In D,, and E,/T for a large number of gas--rubbery polymer combinations, a rule of mixing was derived by Paul [23] on the basis of equation (14) for a polymer blend containing components A and B

613

lnD=t#AInD,+#aInD, + (bR - l)AE,,/RT

(15)

where b is a constant derived from the correlation between the preexponential coefficient Do and the activation energy term E,/T and AE,, is related to the activation energies in the components and mixture by AEM = EL,-

dA EDA

-

tie Em.

(16)

Although, in our case, the phenoxy data of the activation energy are temperature dependent, we have applied equation (16) to the activation energy data, calculated from the slopes of Fig. 2, at the unique temperature at which we have data of both components and the SO/50 blend (418 K). Activation energies for phenoxy, PBA and the blend were, respectively, 48.9, 12.5 and 34.3 kJ/mol. A AE,,, value of 4.18 kJ/mol was obtained from equation (16). According to Paul [23], the quantity of (bR - 1) in equation (15) is negative because bR is smaller than unity. Therefore, a positive AEA,, value results in a lower diffussion coefficient than predicted by the linear logarithmic mixing rule. This is consistent with our diffusion coefficient data at 418 K (see Table 2). The positive AE,, value means that relatively more energy is required for gas molecules to jump from one site to another when the homopoiymers are mixed. This idea is consistent with the previously discussed negative excess volumes generally found in miscible polymer blends. Acknowledgemenls-Authors thank the Basque Government (project No. PGV 9017) for the support of this research. REFERENCES

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