# Experimental Study on the Transport of Light Gas Molecules through Low-Density Polyethylene Films

Authors: Riccardo Checchetto
Journal: International Journal of Polymer Science
 (2018)

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## Abstract

An original experimental procedure for the study of gas permeation process through thin polymer films is presented. Employing mass spectroscopy techniques, this procedure allows the detection of the permeation flux with a signal-to-noise ratio large enough to obtain accurate measurements of the gas diffusivity also in processes with transient transport conditions lasting for short-interval times (~few seconds). The procedure is validated using as test material a thin low-density polyethylene (LDPE) film: the transport of four test gases with different molecular sizes and condensation properties (CO2, N2, D2, and He) is studied in the 295 to 350 K temperature interval. The CO2 diffusivity values well compare with values previously obtained studying the same LDPE film samples by integral permeation technique measuring the time lag value. Original data on the diffusivity of the He and D2 penetrant molecules are reported: in the examined temperature range, the diffusivity values of these small-size penetrants are in the 10−6 cm2/s range and follow an Arrhenius behavior with temperature. The activation energy values for diffusion are 18.8 ± 0.4 and 10.0 ± 0.4 kJ/mol for D2 and He, respectively.


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## Body

## 1. Introduction

The study of mass transport process through polymer films is an important research area given its applicative interest for the development of innovative membranes for gas separation [1] and of gas barrier films to be used in the packaging technology [2]. This topic also presents fundamental interest: gas diffusion occurs by successive jumps of the penetrant molecules between cavities formed in the polymer matrix by the random thermal fluctuations of the macromolecular chains [3, 4]. These cavities constitute the free volume of the polymer which controls structural properties such as the glass transition temperature [5]. Penetrant molecules thus act as sensitive probe to explore the polymer-free volume and its variation, for example, with temperature and cross-linking density [6, 7] or with the addition of filler nanoparticles [8], and to analyze the structure of rigid cavities in biopolymer membranes [9].The gas transport through polymer membranes obeys to the solution-diffusion mechanism [1] which assumes as transport parameters the molecular diffusivity D (units: cm2/s) and solubility Π (units: mol·cm−3·Pa−1) in the polymer layers (the gas permeability Φ is given by the product of gas solubility and diffusivity, Φ=DS). Measurements are carried out by gas-phase permeation technique often using planar membrane samples shaped in the form of a thin disc with a diameter much larger than the disc thickness L. Keeping the sample temperature T constant, at time t=0 (which is the trigger time of the experiment), one side of the planar membrane is exposed to the test gas kept at fixed pressure PHPS. This side of the membrane is called the high-pressure side (HPS). The other side is called the low-pressure side (LPS) and faces an evacuated analysis chamber kept in vacuum conditions. The gas permeation process consists in the transfer of gas molecules from the HPS of the membrane to the analysis chamber through the membrane layers and occurs in three microscopic steps:
(i)
Absorption: penetrant molecules in the gas phase are absorbed by the HPS surface layers of the membrane. Here, their concentration immediately reaches its equilibrium valuecHPS=cx=0,t=ΠPHPS. Here, x=0 represents the coordinate of the HPS
(ii)
Diffusion step: molecules absorbed in the HPS of the membrane diffuse through the membrane layers to the LPS down to their concentration gradient according to the first Fick law,jx,t=−D∂cx,t/∂x; cx,t is the gas concentration at time t in the membrane layers at depth x below the HPS
(iii)
Desorption step: molecules reaching the LPS surface layers of the membrane desorb in the analysis chamber. WhenPLPSgas≪PHPS, the approximation cLPS=cx=L,t=ΠPLPSgas≅0 holds (x=L is the coordinate of the LPS, that is, the membrane thickness)The permeation fluxjt=jx=L,t=−D∂cx=L,t/∂x can be obtained solving Fick’s second equation∂cx,t/∂t=D∂2cx,t/∂x2.The previous diffusion problem admits forjt the following analytical solution:
(1)jt=DΠLPHPS1+2∑n=1∞−1nexp−Dn2π2tL2.Steady-state transport conditions are set whenjt assumes the constant, time-stationary value J=DΠ/LPHPS.Gas molecules permeate through the membrane of surface areaA at a rate Qt=Ajt. Molecules permeated in the analysis chamber form a rarefied gas at thermal equilibrium with the chamber walls at temperature Tcham.The partial pressurePLPSgast of the test gas varies, as a function of time, according to the following relation:
(2)Qt=1RTchamVdPLPSgastdt+SpPLPSgast,where R is the universal gas constant, V is the volume of the analysis chamber, and Sp is the pumping speed of the vacuum system.During the permeation experiments, the pressurePexptin the analysis chamber is measured as a function of time: the analysis of the Pexptcurve by (2) permits to measure the permeation flux jt and to obtain the values of the D and Φ transport parameters.Gas-phase permeation experiments are carried out by integral methods [10, 11]: at t=0, the pumping system is excluded (i.e., Sp=0) and permeated molecules accumulate in the analysis chamber. According to the solution-diffusion model, at time t, the total number of permeated moles mt is given by [12]
(3)mt=A∫t′=0t′=tjt′dt′=ADΠPHPSLt−L26D−2LΠPHPSπ2∑n=1∞−1nn2exp−Dn2π2tL2,and the partial pressure of the test gas in the analysis chamber PLPSgast increases as a function of time as PLPSgast=RTcham/Vmt.In the integral permeation experiments, the pressure in the analysis chamber can be recorded by using low-pressure gauges (in fact,Sp=0 and low-vacuum conditions are rapidly set). Gas transport parameters are obtained by the analysis of the experimental permeation curves Pexptwhen steady-state transport conditions are set, that is, when the Pexptvalue linearly increases with time t.According to the model, in steady state conditionsjt=J=DΠ/LPHPS, thus, mt=ADΠPHPS/Lt−L2/6D and
(4)PLPSgast=RTchamVALDSPHPSt−L26D.The measured rate of pressure increasedPexpt/dt provides the gas permeability Φ=ΠD by the relation dPexpt/dt=dPLPSgast/dt=RTcham/VA/LDSPHPS. The intercept of the straight line fitting the measured pressure data with the time axis, according to (4), defines a parameter called time lag given by τlag=L2/6D: this characteristic time is a measure of the lasting of transient transport conditions and permits the evaluation of the gas diffusivity D.The accuracy of this procedure in the evaluation of the gas transport parameter is limited by the background flowQback due to degassing from the chamber walls (H2O and CO adsorbed during the venting procedure), to small vacuum leaks (H2O vapor, N2, and O2), and to air permeation through Viton O-rings (H2O vapor, N2, and O2). During the permeation test, Qback increases the pressure PLPSbackt of the gases forming the residual vacuum: the pressure PLPStott measured in the analysis chamber is thus given by two contributions Pexpt=PLPSbackt+PLPSgast which cannot be resolved by the total pressure gauge.For a given sample, the accuracy in the evaluation of the gas permeabilityΦ rises by improving the signal-to-noise ratio S/N=dPLPSgas/dt/dPLPSbackt/dt, that is decreasing the sample thickness L. The PLPSbackt term affects the accuracy in the measure of PLPSgast and introduces large relative indetermination in the evaluation of the τlag parameter which impedes to obtain accurate measures of the gas diffusivity studying the fast transport process as it occurs with thin film samples or analyzing the transport of penetrants with high D values or membrane samples made of low-permeability materials [13–16]. Note also that in permeation processes with penetrant diffusivities D in the 10−6 cm2/s order, using film samples with thickness L in the 10 μm range, time lag values are in the few-second order in which the result is thus comparable to that of the response time of the low-pressure gauges.In this paper, we present an original experimental procedure for the study of the gas permeation process which permits accurate evaluation of the gas diffusivity (and permeability) of thin polymer films and processes characterized by short transient times: this often occurs in the permeation of small-size penetrants and in high-temperature processes. The validation of the proposed experimental approach will be carried out using thin films made of low-density polyethylene (LDPE) which is a polymer used as gas barrier in packaging applications [17].Measurements were carried out using test gases with different molecular sizes, molecular masses, and condensation properties and analyzing the transport process up to temperatures close to the LDPE melting temperature. Our measurements permitted us to obtain original data on the diffusivity of the light and small-size D2 and He penetrant molecules, and analysis of the diffusivities permitted the evaluation of the D2 and He activation energy for diffusion which are original data here presented.


## 2. Experimental Part

The study was carried out using membrane samples made of commercial semicrystalline low-density polyethylene (LDPE) kindly provided by ICBM-CNR (Naples, Italy). The X-ray diffraction pattern (XRD) of the LDPE films is presented in Figure1. The spectrum shows sharp, narrow diffraction peaks due to the crystalline fraction of the material at 2θ = 21.1°, 2θ = 23.8°, and 2θ = 36° (see vertical arrows) while the amorphous component gives a very broad peak. The Bragg-Brentano analysis of the XRD peak at 2θ = 21.1° indicated that the average size of PE crystallites is about 12 nm. The crystalline fraction of the LDPE samples, as evaluated by DSC analysis, was 29 ± 1%. The melting temperature Tm of the present LDPE samples was ~380 K [18].Figure 1
XRD spectrum of the LDPE film (Cu Kα radiation, λ=1.5414 Å). The arrow indicates the LDPE reflection peaks.The study of the gas transport properties of the present samples was previously carried out by the procedure described in the introduction, and measurements were carried out in the 290 to 350 K temperature range using H2, CO2, and N2 [18]. Reliable measurements of the permeability and diffusivity values were possible only with the CO2 test gas. Diffusivity values ranged from ~1 × 10−7 cm2/s at 290 K to ~1 × 10−6 cm2/s at 350 K while the activation energy values for diffusion and permeation were 29.7 ± 0.4 kJ/mol and 36.4 ± 0.4 kJ/mol, respectively. Using the H2 and N2 test gases, it was possible to evaluate only the gas permeability because of the large relative indetermination in the short time lag values [18].In the procedure, we are here describing that the permeation experiment is carried out under continuous pumping of the analysis chamber which is done by turbomolecular or sputter-ion pumps: high vacuum conditions are thus maintained during the permeation test.When the condition(5)SpV≫1PLPSgastdPLPSgastdt,is satisfied, then according to (2), the permeation flux jt is directly proportional to the instantaneous value, PLPSgast, of the test gas partial pressure
(6)Qt=Ajt=SpPLPSgast.In the present vacuum system,Sp/V>5s−1 and the condition Sp/V≫1/PLPSdPLPSt/dt are satisfied for each test gas in the examined temperature range.ThePLPSgast curves can be thus converted to experimental permeation flux curves jexpt through the relation
(7)jexpt=1A1RTchamSpPLPSgast.Following this procedure,(i)
the measured value of the permeation fluxJexp in stationary transport conditions permits the evaluation of the penetrant permeability Φ=DΠ by the relation Jexp=J=DΠ/LPHPS
(ii)
the penetrant diffusivityD can be obtained fitting the normalized jexpt/Jexp permeation curves with the curve jnormt=jt/J=1+2∑n=1∞−1nexp−Dn2π2t/L2; see (1)Let us discuss now the advantages of this “constant-pumping” procedure. The continuous pumping of the analysis chamber during the experimental run maintains ultra high- (UHV) or high-vacuum (HV) conditions and, consequently, permits the use of a quadrupole mass spectrometer to detect the permeation signal ILPSgast, that is the ionic current pertinent to the test gas. Knowing the QMS sensitivity for the test gas, αgas, the ILPSgast signal provides a measure of the partial pressure of the permeating gas, PLPSgast=ILPSgas/αgas. The PLPSgast value is thus obtained, as a function of time, without noise contributions due to background flows of any other residual gas component.This experimental procedure consequently allows(i)
very large the signal-to-noise ratioS/N. In fact, S/N=PLPSgast/δPbackgas=ILPSgast/δIbackgas= where the noise δPbackgas=αgasδIbackgas is due to the fluctuations of the background partial pressure Pbackgas of the test gas, only. The S/N is very large for all gases, in particular for those not forming the residual vacuum of the analysis chamber
(ii)
very low detection limit of the permeation flux. For each test gas, in fact, theSpδPbackgas=αgasSpδIbackgas term defines the detection limit (A/Pa). Consequently, the permeation signal can be efficiently detected also studying using low-permeability materials and the permeation fluxes jt can be detected also when Ajt<Qback
(iii)
that the high sampling rate of the QMS, adjustable from 0.5 ms/amu to 60 s/amu (amu: atomic mass unit), permits to recordPLPSgast data with high time resolutionTo test the effectiveness of this “constant-pumping” (CP) approach and for its validation, we used disc-shaped, planar samples with 13.5 ± 0.2 mm diameter and thickness L=53±1 μm. Measurements were carried out in the 295 to 350 K temperature range with PHPS values of 40 kPa using test gas with different molecular sizes and condensation properties: carbon dioxide (CO2), nitrogen (N2), deuterium (D2), and helium (He); see Table 1.Table 1
Chemical-physical properties of the examined test gases [19].
Gas
Critical temperature (K)
Kinetic diameter (Å)
Molecular mass (amu)
D2
38.2
2.89
4
He
5.19
2.6
4
CO2
304.2
3.3
44
N2
126.2
3.64
28Experiments were carried out in a stainless steel analysis chamber pumped by turbomolecular pumps; the detection of the permeation signal is carried out by a QMS equipped with secondary electron multiplier (SEM) and grid-type ion source: this setup permits to detect partial pressures down to 10−12 Pa.A schematic diagram of the system is shown in Figure2(a); for the sake of simplicity, in this figure, the tubular oven used for sample heating is not reported. In Figure 2(b), we present the results of the QMS calibration procedure to evaluate the sensitivity αgas for the examined test gases. Starting from background pressure levels Pback lower than 10−6 Pa, through a calibrated leak valve connected to the gas reservoir, the pressure of the test gas in the pumped analysis chamber is increased by a factor~10 and the corresponding QMS and IG signals were recorded. Repeating this procedure, couples of PLPStvsLLPSgast data were obtained and the slope of the line fitting them provides the value of the αgas parameter. We obtained the following values αHe=125±1 Pa/A, αD2=210±1 Pa/A, αN2=342±3 Pa/A, and αCO2=457±1 Pa/A.Figure 2
(a) Schematic of the experimental apparatus. QMS: quadrupole mass spectrometer; HVS: ultra high-vacuum pumping system; VS1: medium vacuum pumping system (diaphragm pump and molecular drag pump); P1: ionization gauge; P2: low-pressure gauge; V1, V2, and V3: vacuum valves; LV: calibrated leak valve. The membrane sample (M) is vacuum sealed using two Viton O-rings. In this schematic diagram, the tubular oven for membrane sample heating is not reported. (b) QMS calibration curves. The QMS mass signalILPS is reported as a function of the PLPS pressure value for the different test gases. Indetermination is inside the size of the symbol.
(a)
(b)In Figure3(a), we present the mass spectrum of the background vacuum at Pback= 1.2 × 10−6 Pa, after one night of turbomolecular pumping: the spectrum reports the QMS mass signal Ibackgas pertinent to the gases forming the residual vacuum. It can be seen that the background vacuum is mostly composed of water vapor (H2O+, m/e = 18, fragmentation products OH+ at m/e = 17, and O+ at m/e = 16), carbon monoxide (CO+, m/e = 28, fragmentation product C+ at m/e = 12), and molecular hydrogen (H2+, m/e = 2, fragmentation product H+ at m/e = 1) [19]. In Figure 3(b), we report the QMS mass signal for N2 (upper panel) and D2 (lower panel) recorded in the permeation test carried out at 295 K with the described “constant-pumping” procedure: vertical arrows indicate the trigger time t=0.Figure 3
(a) Mass spectrum of the background vacuum atPback=1.2×10−6 Pa after one night of turbomolecular pumping. The dominant contributions are related to the Ibackgas signals pertinent to H2O, CO, and H2 (m/e = 18, 28, and 2, respectively). Their fragmentation products are also reported; see text. (b) QMS mass signals ILPSD2 and ILPSN2 (m/e = 4 and 28, respectively) recorded in the permeation test. Arrows indicate the trigger time of the experiment.
(a)
(b)Looking at the curves fort<0, we observe that the QMS background signals Ibackgas are in the 10−12 and 10−10 A order for D2 and N2 while the δIbackgas fluctuations are ~2 × 10−12 A for both gases: the S/N is thus larger than 10 already in the initial instants of the permeation transient (t>0) and reaches values in the 103 order in stationary transport conditions.TheδIbackgas fluctuations in the 10−12 A order permit to evaluate the detection limit of the present experimental approach by the relation δj~1/A1/RTchamSpαgasδIbackgas. Given the effective Sp values in the 50 L/s order, QMS sensitivity αgas~200Pa/A, see Figure 1(b), and membrane surface area A~1cm2, then δjis in the 10−14 mol·cm−2·s−1 order (Tcham=300K; R=8.3 L·kPa·mol−1·K−1): δj well compare with the upper value of the oxygen transmission rate (OTR) for gas barrier films to be used in the organic light-emitting device (OLED) technology, ~3 × 10−14 mol·cm−2·s−1 [20].The permeation flux is obtained from the curves in Figure3(a) subtracting the background QMS signal Ibackgas from the detected QMS signal ILPSgast and using the relation
(8)jexpt=1A1RTchamSpαgasILPSgast−Ibackgas.


## 3. Results and Discussion

In Figure4(a), we present the jexpt curves as obtained at 295 K exposing the HPS at 40 kPa pressure. In the figure, symbols are the experimental data (relative indeterminations are inside the size of the symbol) obtained by (8) while continuous lines are their numerical fit. All permeation curves are characterized by an initial interval time where penetrant occurs in transient conditions; the permeation flux then reaches a constant value indicating that stationary transport conditions are set. Fits were obtained first measuring the value of the permeation flux in stationary transport condition relation Jexp=DΠ/LPHPS to evaluate the gas permeability Φ=DΠ value and then fitting the normalized jexpt/Jexp curve with the jnormt function to evaluate the gas diffusivity D.Figure 4
(a) Permeation flux curvesjexpt (open symbols) pertinent to CO2, N2, D2, and He obtained at T=295 K and PHPS=40 kPa. Lines are fitting of the experimental curves; see text. (b) Normalized jexpt/Jexp curves (open symbols) pertinent to D2 and He obtained at T=295 K and PHPS=40 kPa. Lines are the jexpt/Jexp curve fittings by the jnormt function; see text.
(a)
(b)Comparing the curves in Figure4(a), we observe that transient transport conditions last for longer interval times with the CO2 and N2 penetrants than with D2 and He which have smaller molecular size. The difference between the permeation curves in transient transport conditions pertinent to the small-size test molecules, namely, D2 and He, can be appreciated by their plots in Figure 4(b) where the normalized jexpt/Jexp permeation flux curves are presented.In Figures5(a)–5(d), we present the experimental jexpt/Jexp permeation curves obtained at temperatures between 295 and 350 K for CO2, N2, D2, and He with PHPS=40 kPa (symbols): the continuous lines are their fitting by the jnormt function. Note that the high signal-to-noise ratio of the present procedure permits to clearly distinguish the permeation curves obtained in the 295 to 350 K temperature range also using the small-size penetrants.Figure 5
(a) Experimentaljexpt/Jexp curves (symbols) pertinent to CO2 obtained at temperatures between T=295 K and T=351 K with PHPS=40 kPa. Lines are fitting of the experimental curves; see text. (b) Experimental jexpt/Jexp curves (symbols) pertinent to N2 obtained at temperatures between T=295 K and T=351 K with PHPS=40 kPa. Lines are fitting of the experimental curves; see text. (c) Experimental jexpt/Jexp curves (symbols) pertinent to D2 obtained at temperatures between T=295 K and T=345 K with PHPS=40 kPa. Lines are fitting of the experimental curves; see text. (d) Experimental jexpt/Jexp curves (symbols) pertinent to He. To avoid confusion, in the figure, we only report curves obtained at 295, 330, and 351 K with PHPS=40 kPa. Lines are fitting of the experimental curves; see text.
(a)
(b)
(c)
(d)The Arrhenius plots of the permeability and diffusivity values are reported in Figures6(a) and 6(b), respectively. Permeability values are reported in practical Barrer units
(9)1Barrer=10−10cm3STPcmcm2scmHg=3.34×10−18molcmcm2sPa.Figure 6
(a) Arrhenius plot of the gas permeability as obtained by analysis of the permeation flux value in stationary transport conditions. Permeability values are presented in practical units (Barrer). (b) Arrhenius plot of the gas diffusivity as obtained by the fitting ofjexpt/Jexp curves; see Figures 5(a)–5(d).
(a)
(b)The activation energy value for permeation and the apparent value of the activation energy for diffusion were obtained fitting the permeability and diffusivity data by the following relations for the gas diffusivityD and permeability Φ:
(10)DT=D0e−ED/kBT,ΦT=Φ0e−EΦ/kBT.ED and EΦ values of the examined test gases are reported in Table 2.Table 2
Activation energy for permeationEΦ and activation energy for diffusion ED as obtained by the Arrhenius plot of the permeability and diffusivity data in Figures 6(a) and 6(b).
Test gas
EΦ (kJ/mol)
ED (kJ/mol)
CO2
36.5 ± 0.5
34.0 ± 0.3
N2
43.2 ± 0.8
38.2 ± 0.5
D2
33.2 ± 0.8
18.8 ± 0.4
He
37.2 ± 0.7
10.0 ± 0.4It is worthy to observe that the diffusivity values have been obtained by the analysis of the whole permeation curve which is composed, given the high sampling rate of the QMS, by a large ensemble of experimental data. This procedure thus allows more accurate evaluation of the gas diffusivity than using the value of a single parameter, as in the time lag method.The obtained diffusivity and permeability values for CO2 as well as the pertinent activation energies are in well agreement with values previously obtained by the “constant-volume” approach [18] and with other literature data; see references therein. The same consideration holds for the permeability values and activation energy values for H2 and N2.To conclude this discussion, it is worthy to comment the obtained results considering the physical-chemical properties of the employed test gases. Considering the diffusion data in Figure6(b) and the penetrant properties in Table 1, we conclude that the penetrant diffusivity through the present LDPE samples decreases by increasing the molecular size. Moreover, comparing the permeability data in Figure 6(a) and the molecular physical-chemical properties in Table 1, we conclude that the gas permeability of the present LDPE samples increases with the critical temperature of the test gas evidencing the important role of the gas condensation properties. In fact, CO2 and N2 have similar molecular size (see Table 1) and diffusivity (see Figure 6(b)) but the CO2 permeability is larger than that of N2. Note that the same considerations hold also comparing the H2 and He transport parameters.This scaling can be discussed considering the theoretical results presented in a recent paper of Dutta and Bhatia on the free volume structure and gas transport properties of polyethylene carried out by equilibrium molecular dynamic simulations [21]. The CO2 and N2 self-diffusivity values indicated by the authors are in the 10−6 cm2/s range, in accord with the present experimental evaluation. They also suggested that the temperature dependence of the penetrant self-diffusivity follows the Arrhenius behavior, as also observed in the present study. Simulations also revealed that the free volume of PE is composed by voids with size ranging from 1.5 to 3 Å. The larger D2 and He diffusivity compared with CO2 and N2 can be explained as consequence of the availability of diffusion sites with a diameter close to the D2 and He molecular sizes and thus is more efficient in accommodating these small-size penetrants.


## 4. Conclusions

We have described a procedure for the experimental study of gas permeation through polymer films. The procedure is based on the measure of the permeation signal in a continuously pumped analysis chamber by a calibrated quadrupole mass spectrometer. This procedure allows (i) very low detection limit of the permeation flux, ~10−14 mol·cm−2·s−1, and (ii) high signal-to-noise ratio in transient transport conditions also when studying polymer films having gas barrier properties. The improved performances permit to resolve the kinetics of the He and D2 transport processes, to obtain their diffusivity values up to temperatures close to those of the LDPE melting and the pertinent activation energies of diffusion. This procedure can be applied for the study of the gas transport processes with the recently developed polymer materials for packaging applications to be applied in fields such as OLED technology. It is also of interest for the community of polymer scientists interested to the study of the correlation between the polymer-free volume structure and transport properties.



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