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Positron annihilation lifetime spectroscopy and diffusion studies of large molecule penetrants into a polyester.


Diffusion of small molecules into polymer matrices has been extensively studied (1). The diffusion of large molecules is less well documented, but is important in printing processes where a dye diffuses into a substrate, as in the case of the Dye Diffusion Thermal Transfer [D2T2] process (2-6). A key step in the D2T2 process is the diffusion of the dye into the receiving polymer film. The transfer of pigment is initiated by a high temperature being created in the printing head, which is in intimate contact with the polymer film. Dye transfer is carried out at high temperature, typically r'400''C and occurs over a short period of time. The receiver layer is usually a lowglass transition temperature ([T.sub.g]) polyester. The durability of the image formed depends on the dye staying in the location in which it is deposited. The prints can be degraded by diffusion of plasticizers etc., into the print. Plasticization of the polyester allows the dye diffusion and blurring of the image. Contact between prints and plasticizers can occur as a result of leaching from the flexible polyvinyl chloride plastic in photo albums, detergents used to clean surfaces, and contact with hands etc.

Positron annihilation lifetime spectroscopy [PALS] allows determination of the size and number of voids at a nano scale and is a direct probe of the free volume. In the case of small molecule diffusion, it has been demonstrated that there is a direct correlation between PALS data and the rates of gas diffusion in the polymer matrix (7-9). This study explores the possible correlations between the PALS characteristics and the permeation behaviour of these large molecules. Previous studies of the D2T2 process have shown that dye diffusion is strongly connected to the Tx of the receiving layer. For the dye to diffuse to occur into the receiving layer there must pre-exist free volume in the matrix.


The diffusion of small molecules into polymeric solids has been discussed by Crank [I]. For many polymer systems diffusion of a penetrant into a polymer conforms to Fickian diffusion. Deviations from the simple behaviour arise when the diffusion occurs into a plasticized matrix or when specific interactions between the polymer and the penetrant modify the nature of the receiving matrix. For simple diffusion, the weight changes which occur in the polymer film on exposure to the penetrant can be described by the Eq. 1, (1):

[M.sub.1]-[M.sub.0]/[M.sub.[infinity]]-[M.sub.0]=4/[square root of ([PI])] (D.t/[[I.sup.2]) (1)

where / is the thickness of the sample, [M.sub.0] is the initial mass of the sample [M.sub.t] and [M.sub.[infinity]] are the masses at time t and at equilibrium.



The polyester was composed of terephthalic acid, isophthalic acid, ethylene glycol, and neopentyl glycol and has a molecular weight of 15,000-20,000 and was obtained from DuPont Teijin Films, Melinex 991 and is commonly used as the receiver layer in the D2T2 process. The polymer was pressed into films; 55 mm X 55 mm X 3 mm in an aluminium mould by application of 100 bar at 170[degrees]C to 4.24 g of polymer for 30 minutes. The pres-sure was then released to allow gas bubbles to come out and then raised to 400 bars for a further 30 minutes. The mould was finally rapidly cooled by plunging in cold water.


The permeants studied were; dioctyl phthalate, (di-2-ethylhexyl phthalate) MWt, 390; 2-ethyl hexylbenzyl phthalate, MWt, 542; nonyl phenol ethoxylate, MWt, 644; isopropyl myristate, MWt, 270; and oleic acid, MWt, 282 (Fig. 1) all the chemicals were obtained from Aldrich Chemical Co. The solubility parameters for the permeants are, respectively, dioctylphthalate, 18.15 (MPa)1/2; 2-eth-ylhexylbenzyl phthalate, 19.58 (MPa)l/2; nonlyphenol ethoxylate, 18.38 (MPa)l/2; isopropylmystate, 16.61 (MPa)l/2; oleic acid, 19.03 (MPa)1/2. The solubility parameter however does not take account of the detailed chemical structure of the molecule and possibility of specific interactions.


Measurements Samples were cut; ~15 mm X ~15 mm X 3 mm and stored in a dessicator for 1 day before use. The sample thicknesses was measured at several locations using a digital micrometer (precision = [+ or -] 0.005 mm) and the mean value recorded. The initial weight of the samples was measured using a Mettler balance PM 100 to an accuracy of [+ or -]0.001 g. The samples were soaked in a screw tight test bottles containing 15-20 ml of the respective permeant in a thermostatically controlled oven at the required temperature. Samples were removed periodically, weighed and the mass change plotted against time allowing estimation of the equilibrium value--[M.sub.[infinity]]. The data was then normalised as indicated in Eq. 1 to determine the diffusion coefficients.


The PALS method used has been described before (10), (11). The system used is a fast slow configuration. A 22NaC1 source was created by sealing a spot of salt between two layers of Kapton using epoxy adhesive. The source was sandwiched between two samples of the polymer. Calibration of the system was carried out using a benzophenone single crystal which has a lifetime time of 331 ps. The lifetime data was least squares analysed using POSITRONFIT (10). Analysis was carried out fixing the two short lifetime components; [t.sub.1] and [t.sub.2] at 0.4 ns and 0.125 ns, respectively. The long lived o-Ps component is well separated from the two shorter lifetime components and is therefore readily deconvoluted. The average hole size was calculated using the relationships derived by Tao (12):


where [t.sub.0]-ps, the o-Ps lifetime (ns) and R, (nm) the hole radius. R0 equals R + DR and DR =--0.166 nm. The cavity volume is then calculated using the relationship:-

[V.sub.c] = (4[pi]/3)[R.sub.3] (3)

A 1 [cm.sub.2] sample of compression moulded copolyester was cut out and sandwiched around the 22Na source. A temperature scan from 30[degrees]C to 70[degrees]C in 10[degrees]C intervals was made and the measurements were repeated three times.

Dynamic Mechanical

Thermal Analysis The Rheometrics dynamic mechanical thermal analyser (DMTA) (13) was used in three point bending mode and operated mei a temperature range --180 to +300[degrees]C and a frequency of 1 Hz. The samples studied were EN-,1-mm thick and the output data was the bending modulus E' and tan 6.


The glass transition of the polyester film was deter-mined DMTA, Fig. 2. The film shows a relatively low value of the bending modulus at room temperature ~7 X [10.sub.8] Pa which drop above the glass transition, [T.sub.g] to a value typical of a rubber ~2 X [10.sub.6] Pa. The peak in the tan 6 is located at 77[degrees]C and is consistent with a low value of the [T.sub.g] required for rapid transfer of the dye into the matrix. The presence of isophthalic acid and neopentyl glycol units in the polymer, inhibit close packing, increase flexibility, and create cavities into which diffusion of the dye can occur.


PALS allows determination of the radius and population of free volume in the polymer. The ortho positronium lifetime and intensity were measured over the temperature range 30[degrees]C to 70[degrees]C, Fig. 3. Measurements could not be performed above 70[degrees]C, as the polyester started to adhere to the source. There is a slow gradual change of the lifetime between 30[degrees]C and 60[degrees]C and then a major increase at 73[degrees]C consistent with the occurrence of the [T.sub.g] at 77[degrees]C. The variation of the oPs intensity increasing slowly up to 60[degrees]C and then apparently becomes almost constant. The hole sizes were calculated using Eq. 2 and the corresponding equivalent volumes using Eq. 3, Table I. These values of the radius and hole size are averaged values and do not reflect the detail of the structure of the free volume created by the polymer chain conformation. The values obtained are similar to those reported for other polymer systems (7), (9), (14).

TABLE 1. Holy radii and volumes calculated from PALS data.

Temperature   Hole    Hole volume
([degrees]C)  radius  ([nm.sub.3)

30            0.2608        0.074
40            0.2638        0.077
50            0.2644        0.077
60            0.2653        0.078
70            0.2743        0.086

Below the [T.sub.g] the void size is dictated by the conformation of the polymer chains. The presence of isophthalate and neopentyl glycol moieties in the polyester will help to disrupt packing of the terephthalate moieties and create the necessary void structure to accommodate the permeating molecules. The hole diameter is twice the radius and of the order of 0.5 nm, which corresponding approximately to the width of a phenyl group. The oPs annihila-tion event is a measure of the dimensions at point at which it annihilates. The problem of relating the oPs lifetime to a void size within a molecular matrix has been considered by Shantarovich (14). He has pointed out that the dimensions measured are the cross section of the cavity and not necessarily the total cavity dimension. Therefore, oPs data provides data on the lower limiting cavity cross section rather than of the whole cavity.

Gravimetric Measurements

Gravimetric measurements were performed to determine how the shape and size of the permeant molecules would influence their diffusion behaviour into the polyester matrix and each permeant will be discussed separately.

2-Ethylhexylbenzene Phthalate. The 2-ethylhexyl benzene phthalate at 30[degrees]C showed relatively fast diffusion into the polyester, Fig. 4. After ~1000 [t.sub.1/2] seconds, the mass uptake plateaus before increasing further up to 1200 [t.sub.1/2] seconds. This is indicative of the molecules plasticizing the matrix prior to swelling the matrix. After 1200 [] seconds, the mass drops indicating that a combination of leaching and densification of the matrix is occurring. Similar behaviour is observed at the higher temperatures, however, the increased rates of diffusion is matched by a decrease in the time at which mass loss is observed. Increase of the temperature lowers the amount of permeant required to achieve plasticization and increases the rate at which the chains can reorganise. The initial diffusion coefficients were estimated, Table 1. Variation of the log of diffusion coefficients against reciprocal temperature allows determination of the apparent activation energy for diffusion. The activa-tion energy calculated changes above 70[degrees]C, permeation at lower temperatures occurring into a glassy polymer whereas above ~70[degrees]C permeation is occurring into a rubbery phase. The high values of the activation energy above Tg implies that the diffusion is coupled with segmental motion of the polymer, whereas below Tg it will reflect the dynamics of the permeant molecule changing its conformation to achieve penetration into a relatively rigid matrix. The loss of mass at longer times reflects the process of dissolution of the polymer matrix which will occur with the initial extraction of low molar mass species. At the higher temperatures, complete dissolution of the polymer occurred at long times.

Dioctyl Phthalate. Dioctyl phthalate has a similar side chain structure to 2-ethylhexyl benzene phthalate but lacks the additional benzene grouping. Its ability to solubilise and diffuse into the polymer is significant less than 2-ethylhexyl benzene phthalate, Figs. 5-7. Whereas, measurements with 2-ethylhexyl benzene phthalate were possible over a temperature range from 30[degrees]C to 80[degrees]C, in the case of dioctylphthalate measurements were only possible between 60-80"C because of the lower solubility and lower rates of diffusion at lower temperatures. The solubility parameter for dioctylphthalate is 18.15 [(MPa).sup.1/2] compared with a value of 19.58 [(MPa).sup.1/2] for 2-ethylhex-ylbenzyl phthalate. This small change in solubility parameter reflects the presence of the additional phenyl groups and surprisingly has a large effect on the ability of the phthalate to enter and swell the polymer matrix. Plots of the mol% weight uptake against [t.sup.1/2] are reasonably linear at 70[degrees]C, however at 60[degrees]C and 80[degrees]C there is a suggestion of a two stage process. At 70[degrees]C, the permeation is taking place very close to the TR of the polyester and diffusion and swelling appear to occur simultaneously. At lower temperatures, permeation occurs prior to swelling, the latter occurring after plasticization has lowered the TR. At 80nC, there appear to be two plateaus positioned at 0.015% and 0.043% weight uptake, respectively. The initial diffusion will occur into a glassy matrix which will swell and allow further permeation to occur. At 50[degrees]C there is initially slow permeation into a rigid matrix followed by a much faster permeation as the matrix is softened by plasticization. Similar changes to those observed at higher temperatures in 2-ethylhexyl benzene phthalate at observed with dioctyl phthalate. Visibly the samples had become very sticky and had undergone significant swelling. The calculated diffusion coefficients, Table 2 indicate a slightly lower value for dioctyl phthalate compared with 2-ethylhexylbenzyl phthalate, consistent with lower activation energies for conformational change in the normal 2-ethylhexyl chain relative to the more sterically hindered 2-ethylhexylbenzyl chain.

TABLE 2. Diffusion coefficients for permeant uptake in polyester

Permeant                              30[degrees]C

2-ethylhexyl benzene phthalate                11.1
Nonvl s henol ethanoate                         --
Isoproply myristate                             --
Oleic acid                                      --
TABLE 2. Diffusion coefficients for
permeant uptake in polyester

Permeant                              40[degrees]C  60[degress]C

Dioctvlphthalate                                            3.48
2-ethylhexyl benzene phthalate                4240          4240
Nonvl s henol ethanoate                         --            --
Isoproply myristate                             --            --
Oleic acid                                      --            --
TABLE 2. Diffusion coefficients for
permeant uptake in polyester

Permeant                              70[degrees]C  80[degrees]C

Dioctvlphthalate                              6.87          9.94
2-ethylhexyl benzene phthalate               42300         77900
Nonvl s henol ethanoate                       2.07          4.75
Isoproply myristate                             --          3.03
Oleic acid                                      --          3.68
TABLE 2. Diffusion coefficients for
permeant uptake in polyester

Permeant                              [E.sub.a.sup.1]  [E.sub.a.sup.2]
                                      KJ-[mol.sup.-1]  KJ-[mol.sup.-1]

Dioctvlphthalate                                   --              8.0
2-ethylhexyl benzene phthalate                   69.9             11.3
Nonvl s henol ethanoate                          16.9              9.7
Isoproply myristate                                --               --
Oleic acid                                         --               --

Nonyl Phenol Ethanoate. At 60[degrees]C, nonylphenol ethanoate exhibits a much higher rate of diffusion than that observed for dioctylphthalate, reflecting the lower cross section of this molecule and hence its greater ability to adopt favourable conformations for diffusion, Figs. 5-7. Nonlyphenol ethoxylate has a solubility parameter of 18.38 [(MPa).sup.1/2] which is higher than that of dioctylphtha-late with a value of 18.15 [(MPa).sup.1/2] but lower than that of 2-ethylhexylbenzyl phthalate with a value of 19.58 [(MPa).sup.1/2]. Its greater ability to solvate the polyester is evident in its permeation behaviour, but unlike 2-ethylhexyl-benzyl phthalate it is unable to swell the matrix and cause dissolution of the polymer. Calculated diffusion coefficients allows estimate on activation energies for permeation of 9.7 kJ/mol, which is higher than that observed in dioctyl phthalate but lower than the value observed for 2-ethylhexylbenzyl phthalate.

Isopropylmyristate. Appreciable diffusion was only detected at 80[degrees]C, where the t'12 plot shows once more an apparent plateau between the initial permeation of the solvent and the latter slightly faster diffusion behaviour, Fig. 4. Isopropylmystate with a solubility parameter of 16.61 [(MPa).sup.1/2] has the lowest value of the permeants studied and this is reflected in the low levels of diffusion observed. It is very clear that the solubility parameter is critical in understanding whether or not these large molecules will undergo significant diffusion into the polyester matrix.

Oleic Acid. Oelic acid with a solubility parameter of 19.03 [(MPa).sup.1/2] might be expected to exhibit behaviour similar to that of nonlyphenol ethanoate, however its behaviour is closer to that of isopropylmyristate and the initial permeant uptake being slightly faster but the subsequent diffusion is slightly slower, Fig. 5. The overall characteristics of the diffusion behaviour of the two permeants into the polyester matrix have a similar form despite having significantly different solubility parameters. Oleic acid will form a dimer in the solid phase and this may inhibit favourable interactions with the polyester.

Molecular Modelling

In an attempt to gain a greater insight into the relationship between the molecular sizes quantum mechanical calculations were performed to determine the lowest energy conformations for the permeant molecules were performed using Hyperchem Version 4.5. The lowest energy conformations are shown in Fig. 8. Using this conformation it is possible to construct the volume which such a molecular structure would occupy, Table 3. The conformations and values of cross-sectional areas calculated correspond to the minimum energy state for the isolated molecule and do not take in to account any interactions which might occur with the polymer matrix.

TABLE 3. Values of the periodic box volume and dimensions
calculated for the permeant molecules.

              Periodic box  Periodic
Temperature   volume        dimensions
([degrees]C)  ([nm.sup.3])  (nm)

30                   0.906  1.06 x 0.77
                                 x 1.11
40                   0.901  1.06 x 0.78
                                 x 1.09
60                   0.912  1.11 x 0.74
                                 x 1.11
70                   0.976  1.16 x 0.61
                                 x 1.38
80                   0.987  1.13 x 0.74
                                 x 1.18
30                   2.056  1.14 x 0.82
                                 x 2.20
40                   2.057  1.13 X 0.82
                                 X 2.22
60                   2.023  1.12 x 0.81
                                 X 2.23
70                   2.096  1.14 x 0.81
                                 x 2.27
80                   2.041  1.14 x 0.81
                                 x 0.21
Nony pheno'
30                   4.793  1.44 x 0.86
                                 X 3.87
40                   4.857  1.45 X 0.87
                                 X 3.85
60                   4.917  1.45 x 0.89
                                 x 3.81
70                   4.993  1.46 X 0.90
                                 X 3.81
80                   5.022  1.46 X 0.91
                                 X 3.78
30                   0.514  0.59 x 0.40
                                 x 2.18
40                   0.558  0.59 x 0.45
                                 x 2.10
60                   0.607  0.79 x 0.39
                                 x 1.97
70                   0.650  0.67 x 0.48
                                 x 2.02
80                   0.647  0.69 x 0.47
                                 x 2.00
Oleic acid
30                   0.655  0.82 x 0.36
                                 X 2.22
40                   0.679  0.83 x 0.36
                                 x 2.22
60                   0.702  0.87 x 0.37
                                 X 2.18
70                   0.707  0.88 x 0.37
                                 x 2.17
80                   0.716  0.90 x 0.37
                                 x 2.15

Higher energy conformations will usually reduce the size of the molecule by the alkane chains adopting more gauche conformations. This "periodic box" is an upper estimate of the volume required, as it does not allow these high aspect ratio molecules to fit in between other molecular entities.

Comparison of the data from the calculations and that from oPs studies indicate that the concept of a molecule hopping into a void is not consistent with the size of hole available in the polymer matrix. Looking at the permeants, the cross section of the alkane chain is comparable to that of the hole. The oPs is a measurement of the average void size measured on a timer scale of [10.sup.-9] sec where as the diffusion process is the integration of motions taking place over a considerably longer period of time. It is therefore obvious that the molecule rather than moving by a single jump must slither through the polymer matrix.

In the case of isopropyl myristate and oleic acid, the cross section which the molecule presents is comparable with the dimensions measured by oPs, however, the length dimensions are significantly greater than the measured cavity dimensions which indicates that the diffusion process must be rather like a snake entering a tube. In the case of dioctyl phthalate, 2-ethyl hexylbenzyl phthalate and nonyl phenol ethoxylate their dimensions are all greater than the void size measured by oPs which is consistent with the observation that these molecules must undergo significant interactions with the polymer matrix prior to diffusion occurring and consequent swelling increases the void size allowing diffusion. Since the polymer and permeant both contain phenyl groups, favourable [pi]-[pi]* interactions provides a mechanism for swelling the polymer matrix. On this basis, the 2-ethylhexyl benzene phthalate with a structure which closely resembles that of the polymer chain will have a greater ability to swell the polymer than dioctylphthalate. Swelling of the surface layer will then facilitate diffusion of the permeant into the polymer matrix.

Molecules such as isopropy myristate, and oleic acids lack the ability to undergo interactions with the phenyl ring structure of the polyester and rely totally on being able to find a void into which the alkane chains can permeate. The net result is that lower diffusion coefficients are observed for these molecules, although their apparent cross sections are very significantly smaller than those of the phthalates. Nionyl phenol ethanoate, although dimensionally a much longer molecule, has a slightly higher diffusion coefficient than either isopropyl myristate or oleic acid, because the combination of phenyl and ether groups will enhance its ability to swell the polymer. The gravimetric data suggest that permeant molecules enter the matrix and induce swelling which will itself increase the void size distribution and allow faster diffusion. This proposal is consistent with the observation in Figs. 4-6 and the sticky appearance of the polymer in the latter stages of the experiment.


This study indicates that it is not the size of the molecule relative to the void sizes present in the matrix, but the ability of the permeant molecule to interact with the matrix which controls diffusion. This situation is very different from that often encountered with small molecule gas diffusion through polymer membranes, where good correlations can be found between the voids sizes and the relative rates of diffusion. In the current system, the ability to swell the polymer which is dictated by the distribution of phenyl rings, has a very profound effect on the ability for the molecules to enter the polymer matrix and then to undergo diffusion within it. Comparison of the theoretically predicted size data implies that the motions are probably cooperative between the permeant and the motion of the backbone of the polymer chain. This proposition is consistent with the idea that the diffusion rates are significantly increased at or above the [T.sub.g] and implies that the ability of the permeant to enter the polyester matrix depend critically on their chemical structure and not on size.

Comparison of the size of the molecules and that of the void size measured by oPs measurements divides the molecules into two groups. Isopropylmyristate and oleic acid exhibits cross sections which would allow the molecules to slither into cavities. The remaining molecules have cross sections which are large than the available void size and must swell the matrix before diffusion can occur. The permeation behaviour is influenced by the available free volume but dominated by the solubility characteristics of these molecules.


S.A.W. thank ICI Image data and the EPSRC for financial support during the period of this project.


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Correspondence to: Richard A. Pethrick; e-mail:

Shelia A. Ward, Richard A. Pethrick

WestCHEM, Department of Pure and Applied Chemistry, University of Strathclyde, 295 Cathedral Street, Glasgow G1 1Xl, UK

DOI 0.1002/pen.23141
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Author:Ward, Shelia A.; Pethrick, Richard A.
Publication:Polymer Engineering and Science
Article Type:Report
Geographic Code:4EUUK
Date:Sep 1, 2012
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