MOLECULAR PACKING IN SURFACE LAYERS

When a filler is incorporated into a polymer, the conditions of molecular packing worsen and packing density diminishes because of conformational restrictions described above. The polymer transforms to a less stable state, from a thermody-namic point of view. It seems proven that the loose packing is the result of the re-tardation of relaxation processes during the formation of a filled polymer. The retardation depends on the nature of solid and polymer. The main factors deter-mining the retardation of the relaxation processes are the energy of interaction between a filler and a polymer (adhesion energy), cohesion energy of a polymer (intermolecular interactions in the polymer matrix), and the flexibility of poly-meric chains. The statement validity was experimentally evaluated^19,20 for three polymers having different chemical structure - PS, PMMA and poly(dimethyl siloxane) (PDMS). Two of these polymers (PS and PMMA) have almost equal values of the parameter of the thermodynamic flexibility,σ. At the same time, polymers have various cohesion energy densities, Ec. The other se-lection - PS and PDMS - have almost the same cohesion energy density but dif-ferent flexibility, as follows from data in Table 1.

Such choice of polymers gives a possibility to establish contributions to the changing density packing in the surface layer at the expense of chain flexibility and the chemical nature of a polymer, i.e., the presence of some functional groups capable of interaction with the surface. The density of packing was inves-tigated by the method of molecular probe.^19,20Figure 3.2 presents the data on the dependence of the density of a polymer in the layerρ_sand in the bulkρ_p on the distance from the surface. The density ratio was calculated from the experimen-tal data based on the spectral shift of probe molecules, whereas the distance Table 3.1: Cohesion energy density and flexibility

Polymer E, J/cm σ

PMMA 556.4 2.14

PS 305.0 2.22

PDMS 322.6 1.47

from the surface was estimated from the concentration of probe molecules, which according to the theory is proportional to the layer thickness or to the dis-tance from the surface.

Two surfaces have been taken as supports: quartz (high surface energy) and poly(tetra-flouroethylene) (Teflon^TM) (low surface energy). It is seen that for all polymers there is some increase observed in the packing density in layers ad-jacent to the surface, independent of its surface energy. This effect may be at-tributed to the orienting action of the surface. The increase in density in this layer is of the order of 3-5% for all polymers. The difference in the surface influ-ence on the packing density for supports of high and low surface energy is the greatest for PMMA having higher Ecandσand is very low for PDMS. From the comparison of these data, it is seen that the difference in value Ecandσ deter-mines the character of macromolecular packing. The density ratio, the layer thickness, and the degree of the influence of the surface energy of support are functions of these two parameters.

It was found that the structural rearrangements in the surface layer for films formed at the Teflon surfaces is restricted by the formation of a more dense layer near the interface. The thickness of this layer for PDMS is 2-3, for PS and

Figure 3.2. Changes in the packing density in surface layers with distance from the surface: PDMS (a), PS (b), PMMA (c). Dotted lines - layers on poly(tetra-fluoroethylene), solid lines - on quartz.

[Adapted by permission from Y. Lipatov, E. Moisya, and G. Semenovich, Polymer, 16, 582 (1975)]

PMMA, 3-4µm. For more flexible PDMS on both surfaces, the orienting influence of the surface di-minishes at thicknesses larger than 2-3µm, and density of packing becomes equal to that for the polymer in bulk. On the contrary, for PS and PMMA, the structure of a layer on a substrate with high surface energy is rather complex. The regions of high density near the interface are re-placed by the region with the same density as in bulk (transition layers), followed by the region where the packing density is lower compared with bulk (loose packing). The total thickness of the surface layers on the support of high surface energy, where the changes in density are ob-served, is 30µm for PS and 60µm for PMMA.

These data show that under the influence of a solid, surface layers are formed having a complex structure and a definite density profile. The char-acter of this profile depends on the three parame-ters: chain flexibility, cohesion energy of a polymer, and surface energy of a support. How-ever, in all cases the layer nearest to the surface has higher density, compared with bulk.

The non-homogeneous structure of the sur-face layers follows also from the data on the dependence of the specific volume of the system on the filler concentration.^21,22Figure 3.3 shows such dependence for a PS-glass powder system. It is seen that specific volume, v, for highly loaded samples exceeds the additivity rule. This effect cannot be the result of the forma-tion of voids in loose-packed aggregates of filler particles which are not available for polymer molecules. The extrapolation of the linear part of the dependence of v on volume fraction of filler,ϕ toϕ =1 gives the value of v = 0.420×10^-3 kg/m, which coincides with the specific volume of a glass. Thus the character of the changes of v in dependence on the filler concentration confirms the transition of PS into the state of a loose-packed surface layer. In the region,ϕ >0.3 all polymer

Figure 3.3. Dependence of specific volume, v, of filled PS on the filler amount, W, at various temperatures (K):

1-297, 2-365, 3-425, 4-471. 1’-4’- corresponding additive dependencies.

may be considered as being in the state of a sur-face layer. The value ofϕcorresponds to the ef-fective thickness of the interlayer between two filler particles, which is about 1.5×10^-6m.

It may be postulated that the change of the structure in filled polymers (change in the packing density) is connected with formation of disjoining pressure in the interlayers of a poly-mer between filler particles. According to defi-nition,²³ the disjoining pressure, P_d, is an excess of a phase pressure in the thin liquid film near the interface, Pph, in relation to the pressure in the bulk, P₀, i.e., P_d=P_ph−P₀. Dis-joining pressure is a result of the change in the free energy of a film during the approach of two restricting surfaces (i.e., with diminishing film thickness, h), thus:

where S is the interphase surface and F is the Helmholz free energy.

The curves of dependence of the relative free energy of PS and PMMA filled with glass powder on the effective thickness of the interlayer between two filler particles are given in Figure 3.4. The values∆F/ kT were calculated according to the formula:

which includes parameters of Eq 3.7. The monotonous increase in the free en-ergy with decreasing h (Figure 3.4) reflects the repulsion of particles due to the positive disjoining pressure. A quantitative assessment of the change in the

Figure 3.4. Dependence of the relative free energy,∆F/kT, for filled PS (1) and PMMA (2) on the effective thickness, h, of the polymer interlayer.

structure of the polymer which takes place in the processing of the polymer in the presence of a filler can be made based on the determination of the spe-cific surfaces and pore volumes, which makes as-sessment of packing density of macromolecules possible.²⁴ For this purpose, the isotherms of the sorption of vapor of the solvent (inert in relation to polymer) may be measured.²⁵

Figure 3.5 shows isotherms of sorption of methyl alcohol vapor (p1, the pressure of vapor over the solution, and p0the pressure of the saturated vapor) by films of PMMA containing varying amounts of filler. The isotherms for filled PS have the same shape. It may be seen that the addition of filler leads to an increase in adsorption which grows as filler content increases. Calculation shows that the rise in adsorption cannot be due to sorption of vapor on the filler and is governed, con-sequently, by changes in the packing density. It was also shown that specific surfaces and pore vol-ume calculated using the BET method increase with incorporation of the filler. These data indicate a powerful influence of the filler on the processes of structure-formation taking place in the processing of a polymeric material in the presence of a filler.

Moreover, the reduction in the packing density in the presence of a filler is considerably more marked with the specimens cast from solution than those prepared by molding. This is because in the processing of a polymeric material the interaction of the polymer molecules or aggregates with the surface of the filler alters the conditions under which relaxation occurs. Because of the inter-action of the chains with the surface, there is a limitation in the mobility of the chains, leading to loose packing. It is quite evident that in this case, where relax-ation processes in the filled polymer are facilitated, the filler will have less effect on the density. Some thermodynamic problems connected with sorption of vapor by filled polymers are discussed below (Chapter 4).

Figure 3.5. Isotherms of

For crystalline polymers, the incorporation of filler also leads to changes in density of the amorphous phase of polymer. If the density of disordered regions in filled semi-crystalline polymer,ρ_d, is an additive sum of the density of the dis-ordered region in the bulk,ρ_o, and in the surface layer,ρ_s, then we have:

ρ_d =ρ ν ρ_s + _o(1−ν ρ) = _o −(ρ_o −ρ ν_s) [3.9]

whereνis the fraction of a polymer in the surface layer. This value is connected with the volume fraction of a polymer in the filled system:

(r + )

r 1= (1 )

δ 3 νϕ ϕ







 − − [3.10]

where r is the radius of a filler particle,δis the thickness of the surface layer, and ϕ is the volume fraction of a filler. From Eqs 3.9 and 3.10 we have:

ρ ρ ϕ

d = o −K(1ϕ− ) [3.11]

where

K = ( ) (r + )

o r r

3

ρ −ρ  δ





 [3.12]

If these assumptions are correct, then the dependence ofρ_don the ratio of (1-ϕ)/ϕ should be a straight line with a slope K which cuts off, on the ordinate axis, the valueρ₀corresponding to the density of unfilled amorphous polymer.

Such dependence is presented in Figure 3.6 for filled polyethylene. From this de-pendence, the following values were calculated: ρ₀ = 880±15 kg/m³ and K=4400±100 kg/m³. The value ofρ₀corresponds to the density of amorphous re-gions in unfilled polyethylene.

It is important to evaluate the thickness and the density of the surface lay-ers in filled polyethylene. The dependence ofρ_s/ρ₀onδ/r is presented in Figure

3.7. It is seen that at high value ofδ/r, the ratioρ_s/ρ₀asymptotic approaches unity, whereas atδ/r < 3 that ratio sharply de-creases. Because, as follows from Figure 3.7, the inequalityρ_s/ρ₀>0 is valid, the ratioδ/r is more than 1. More correctly, these values may be estimated if we as-sume the additivity of densities of sur-face layers around filler particles and polymer density at the condition that the distance, L, between filler particles is L 2≤ δ. The L may be calculated from the

whereϕ_Mis the volume fraction of a filler at maximum dense packing of filler particles in the polymer (for polydisperse particlesϕ_M= 0.81). Because, as fol-lows from Figure 3.6, Eq 3.11 is valid at fumed silica content up to 10 wt%, using value (1 -ϕ)/ϕ= 0.01 andϕ_M= 0.81, we find from the above relations thatδ/r=1.2, which corresponds to the thickness of the surface layer ~150 Å, if the diameter of the fumed silica particle is 250 Å. From Figure 3.6, we also find that atδ/r=1.2, the ratioρ_s/ρ₀= 0.5. Finally, from Eq 3.10, it follows thatν =0.1.

In a previous publication,²⁷the kinetics of the isothermal crystallization of oligoethyleneglycol adipate, filled with glass powder, was studied and the re-duced packing densities Va/Vas(Vaand Vasare specific volumes of amorphous phases in bulk and surface layers) calculated, based on the average distance be-tween the filler particles, L (Figure 3.7). It was found that in the investigated range of L values, the regions with varying density arises, i.e., alternations of more dense and less dense regions are observed. Such picture can be explained by the non-equilibrity of the surface layers (see below). It may be predicted that a real profile of the curve of reduced packing density consists of alternating

max-Figure 3.6. Dependence of the density of distorted regions in polyethylene,ρf, on the amount of fumed silica:  - initial samples, l - heat treated samples.

imum and minimum, with step-wise decrease in their intensity with increasing L.

The thicknesses of the surface layers of some elastomers are 100 Å and depend on the surface nature.²⁸ For elastomers the formation of more dense and less dense layers was also ob-served. The loose layer has the greatest thick-ness. The values determined by the ellipsometry method depend on temperature, because with growing temperature the molecular mobility of chains increases, and because of the increase in the surface of the molecular contact, the density of the layer increases. Much less data are avail-able on packing density in filled crosslinked polymers. For cured epoxy resin it was found²⁹ that the properties of the surface layer at the in-terface with a solid depend on the curing condi-tions. The ordered surface layer has a thickness of 0.5-0.6×10^-3 m, which is by one order higher when compared with linear polymers.

3.4 METHODS OF EVALUATION OF THE FRACTION OF SURFACE LAYERS IN