Structural changes during elongation of polymer solutions

Journal of Non-Newtonian Fluid Mechanics, 23 (1987) 49-72 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

STRUCT’URAL OF POLYMER

J. FERGUSON,

49

CHANGES DURING ELONGATION SOLUTIONS

N.E. HUDSON

Fibre and Textile Research Unit, Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow GI IXL (Gr. Britain) and B.C.H. WARREN C.D.E., Porton Down, Salisbury SP4 CnrQ(Gr. Britain) (Accepted June 30, 1986)

Summary During elongational flow experiments on polymer solutions certain anomalous examples of flow behaviour have been noted. These are, (1) a non uniform velocity profile in the radial direction in strongly non-Newtonian fluids being elongated at high rates, (2) the loss of tack in the filament as rate of elongation increased, (3) the bouncing of the filament off a rotating drum at high elongation rates, and (4) the development of sustained rubber-like lateral vibrations in the fluids elongated at high rate. In addition, droplet formation occurred on the surface of the solutions which were elongated rapidly then suddenly stopped. Photography showed that the filaments continued through these droplets. When captured and dried, it was observed that the filament contained the bulk of the solute. The droplets appeared to have only a low concentration of polymer. On the basis of the photographic evidence and the thermodynamics of complex formation between elongated polymer chains, it would appear that complexation of the chains is occurring at high elongation rates. This could partly account for the strain hardening encountered during elongation of many polymeric fluids. Where solubility parameter difference between polymer and solvent was large, the complex formed could come out of solution forming a gel and a solvent rich phase.

0377-0257/87/$03.50

0 1987 Elsevier Science Publishers B.V.

50

Introduction It is generally thought that when a polymer solution or melt is elongated, the change in elongational viscosity with strain or strain rate can be attributed wholly to changes in polymer orientation, shape, and entanglement density. The authors have been engaged in carrying out elongational viscosity studies for a number of years and have observed certain anomalous flow characteristics. Several of these were demonstrated in a film shown at the Conference. These anomalies strongly indicate that, under elongation at high strains or strain rates, flow induced gelation (or complexation) of the polymer molecules may be occurring. In the extreme case, this could lead to solvent exclusion producing a phase change within the extending filament. If this is the case, then the changes of elongational viscosity with strain or

2%PEO

in wat*,

Elongational

Viscosity

Strain

Y

Fig. 1. A typical elongational viscosity-Hencky strain curve for many polymer solutions, showing strain hardening. This example shows a 2% solution of PEO in water, measured on the Sangamo Elongational Viscometer. Experimental conditions: drum speed 0.22 m.s-‘, filament length 43 mm, mass flow rate 64 mg.s-‘.

51 strain rate will be significantly affected. In particular, the causes of the so called “strain hardening” or increase in elongational viscosity (Fig. 1) with strain rate, would need to be reassessed. It is the purpose of this paper to present experimental findings which lend credence to the above hypothesis, together with preliminary theoretical arguments which support it. Two major phenomena would appear to contribute to gelation; these are (1) stress induced alignment of the macromolecules in a flow field, and (2) complexation by a “zipping up” process induced by co-operativity of adjacent chain segments. These effects may be enhanced by a concentration of molecules caused by stress induced diffusion. Stress induced diffusion The majority of the work on stress induced diffusion of macromolecules has been conducted under conditions of shear. It was first observed by Garner and Nissan [l] that since groups of molecules increase their entropy by moving towards regions of lower strain, a spontaneous tendency will be created, in jets of fluid emerging from a nozzle, for molecules to move inwards. They claim to have verified this by experiments on rubber dissolved in benzene. Tirrell and Malone [2] investigated conditions in capillary flow for polymer migration (diffusion), which they attributed to entropic effects. Under optimum conditions, a radial fractionation of the polymer could occur not only in solution but also with polymer melts. The arguments were developed by Metzner et al. [3] who determined, for aqueous Separan solutions, the concentration of polymer in a static region next to the main flow through a circular tube. For flow of the same solutions through a screen simulating a porous bed, they observed fibres of gelled polymer forming immediately downstream of the screen. Using a kinetic approach, Aubert and Tirrell [4] showed that macromolecular diffusion was to be expected in non-homogeneous flow fields. This was later extended by Sekhon et al. [5] and a number of other workers. The logical conclusion of an increasing concentration gradient would be that gelation of the concentrated phase would occur. As mentioned earlier, few reports have appeared on this phenomenon in purely elongational flow. Mackley and Keller [6] have reported strain induced crystallisation of high density polyethylene in xylene in an impinging flow, in the region dominated by extensional deformation. Janssen and Janssen-van Rosmalen [7] used a thermodynamic approach to describe the theoretical growth of a long fibre from a seed polymer in the centre of a capillary. The dominant mode of deformation was elongational at the tip of the growing fibre inducing further gelation, from solution, of the polymer.

52 Complexation Complexation is a process by which secondary bonds are formed between polymer molecules. These can arise from Coulombic forces, hydrogen bonding, hydrophobic interactions, Van der Waal’s forces, etc. No covalent bonds are formed and the complex formation can often be reversible. This is in contrast to covalent crosslinking. Generally, complexation will depend not only on the strength of interaction, but also on the size of the polymer molecules and the degree of “fit”, that is the ability of one molecule, structurally, to align its interacting groups with those of its complexing partner. It should be noted that complexation is generally considered to take place between molecules of different chemical structure, for example poly acids and poly bases, but this does not preclude interactions between portions of the same polymer chain, or different molecules of the same polymer. Challa and Tan [8] have, for example, shown that isotactic and syndiotactic polymethyl methacrylate (PMMA) form gelled complexes when mixed in solution. A considerable body of literature exists on polymer-polymer interaction and formation of complexes in solutions of interacting polymers. While it is not necessary to consider these in detail, two particularly useful reviews are worth quoting. These are by Kabanov and Papisov [9] and by Tsuchida and Abe [lo]. Both reviews deal primarily with interaction between dissimilar macromolecules. The former paper describes the high selectivity of interactions in terms of polymer molecular weights, whilst the latter concentrates more on the intermolecular forces involved. It is worth noting that the conclusions drawn about interactions between dissimilar polymers apply equally well between chains of the same polymer. Tsuchida and Abe in particular point out that the configuration and conformation of macromolecules in solution play a significant part in aggregation, together with secondary binding forces, solvation, steric factors and interpenetration. All of these parameters are influenced by a strongly elongational flow field. Thermodynamic

aspects

It is well known that when two dissimilar their ability to complex is given by (polymer,)

+ (polymer,)

+ complex.

polymers

are mixed in solution,

(1)

A typical free energy diagram for this reversible reaction is shown in Fig. 2. The driving force for complexation is given by AG = G, - G,, where G, is the total free energy of the system of two polymer solutions before any com-

53

0

I 50

0

Fig. 2. A schematic free energy diagram for the complexation reaction given in eqn. (1). The free energy, G, is plotted against the percentage number of complexed molecules, NAB. G, is the total free energy of the separate polymers in solution, G, is the free energy of the complex. For complexation to take place, GS > G,. The two possible cases shown, (a) and (b), are discussed in the text.

plexation takes place, G, is the total free energy when all molecules have complexed, and G is the equilibrium free energy, which is a minimum. The value of NAB, the number of complexed molecules, at equilibrium is of course affected by such factors as temperature and the solvent. Case (a) occurs when all the molecules have complexed (if Gc < G,). The strength of secondary bonds varies in the order: Coulobic (electrostatic) interactions > hydrogen bonds > Van der Waal’s forces > hydrophobic interactions. The polyelectrolyte complexes formed, for example, between polyacrylic acid (PAA) and poly(4-vinyl pyridine) contains a strict 1 : 1 ratio of base molar repeat units, all polymers being complexed. PAA also complexes by hydrogen bonding with poly vinyl pyrrolidone, in a 1 : 1 ratio [ll]. These are cases in which G, < Gs. If Gc < Gs then no complexation occurs. Another possibility is case (b), where the minimum free energy at equilibrium occurs at some intermediate value of NAB. For example, complexation between PAA and polyethylene oxide (PEO) is only complete above a PEO molecular weight of 6000. Below this value little complexing occurs in

54 solutions at rest [12]. It has been shown [9] that the change in free energy, AG, is made up of two components, AG=AG,+AG,.

(2)

AG, is the change in conformational

free energy, given by

AG, = AH, - TAS,,

(3)

where AH, is the change in enthalpy, AS, is the change in conformational entropy, and T is the absolute temperature. Since the conformation on complexing involves a substantial change in shape for randomly coiled molecules in solution, AS, will be large. AH,, in contrast, is relatively insignificant, and independent of the number of molecules complexed. AG, is the change in configurational free energy, given by AG, = AH, - TAS,,

(4)

where A H2 is zero for changes in configuration, and AS, is the change in configurational entropy, which is related to the probability of the polymers being in solution or in complex [9]. At equilibrium, aAG -= a&B

0 (5)

’

Kabanov

and Papisov

Kf’ = exp( -n

AGy/RT),

used this equation

to determine (7)

the equilibrium constant for complexation, where AGF is the free energy change in the standard state, and n is the number of repeat units in the complexed polymer. The thermodynamics do not say anything about the rate at which complexation takes place, merely that it is thermodynamically feasible. For many mixtures of polymers in solution, the rate of complexation is so small that no appreciable changes would have occurred during the timescale of the flow experiment. In a simple polymer solution at rest, the total free energy is less than that of the polymer and solvent before dissolution, so the free energy of mixing, AG, < 0. If there is a positive interaction between polymer and solvent, AH, is negative and solution occurs. If dispersion forces only are involved, solution will depend upon the magnitude of AH,,,. If the mixing is endothermic, then the enthalpy of mixing is given by [13] AH,

= v,+;(S, - S,)*,

55

Fig. 3. A schematic diagram of the complexation process at rest. Repeat units of entangled macromolecules can start to complex if they move close together, providing interactions between them are possible. Once started, complexation proceeds by a zipping-up process. S: solvent molecules, which are excluded from the region between the complexing macromolecules.

where C/Iis the volume fraction, V the molar volume, and 6 the solubility parameter, of solvent, s, and polymer, p. Therefore, there may be a minimum in the free energy curve away from G,, the total free energy of the solution. A small degree of complexation could then take place in such a solution at rest. Figure 3 illustrates the progression of complexation in a solution at rest. The formation of a secondary bond between interacting groups on neighbouring chains will bring adjacent groups into close proximity so that they, in turn, can interact. A “zipping up” process then takes place which is controlled by molecular size, conformation, configuration and strength of intermolecular forces. Obviously, polymer entanglements and chain flexibility are also going to influence the rate at which complexation occurs.

56

Elongation

Complexation

Fig. 4. A schematic diagram of the complexation process during elongational many of the entanglement junctions have been destroyed by the flow, some entanglements will still exist. Alignment of the macromolecules enhances the process. Shorter chain molecules do not tend to take part in the complexation they, together with the solvent molecules S, will tend to be excluded from the regions.

flow. Whilst long-lifetime complexation process, and complexation

For exothermic reactions, however, AH, < 0, and polymer-solvent bonds will be much stronger than polymer-polymer bonds, so that complexation is unlikely. In a flow field, the free energy of the solution will be increased. At the same time, the configurational entropy change, AS,, will be decreased considerably. These factors could combine to create a situation in which AGF K 0, and complexation would then be thermodynamically feasible. In an extensional flow field, the same forces as at rest would be present, but where pronounced orientation occurs, the complexation process would be greatly facilitated (see Fig. 4). This of course implies that the lifetime of the entanglement junctions should be longer than the time taken for zipping up. For small molecules, this requirement will not be met, so that these will

57 not be included in the oriented complex. This fractionation will be further enhanced by the fact that small molecules have been shown to be inherently less able to complex than longer polymer chains [9]. Solubility parameter The concept of solubility parameter is not one logical literature. Nevertheless, it plays a key solubility characteristics of a polymer in a solvent, authors feel that its significance and measurement The solubility parameter has been defined in energy density [ 131.

commonly used in rheorole in determining the and for this reason, the should be described. terms of molar cohesive

6 = ( - E/V)“.5, (8) where E is the molecular cohesive energy, and k’ is molar volume. It is therefore related to intermolecular forces of attraction and hence to the ability of a material to dissolve or to crystallise. The closer the solubility parameters of a solid (for example a polymer) and a potential solvent, the more likely are they to form a solution. Conversely, the greater the difference, the more likely a polymer will be to come out of solution. If the solubility parameters of solvent and polymer are very different, complexation could be sufficient to exclude solvent, giving a gel, or, in the extreme case, polymer precipitation, with a two phase structure formed. The solvent rich phase would then be forced to the outside of the extending filament. This would lead to the observed changes in physical properties at high rates of extension, that is, changes in tack, and non-uniform velocity profile. In particular, when elongation is suddenly stopped, surface tension would take over, forcing the solvent rich sheath into droplets around the persistent polymer gel. This model would also account for spinnability, that is, at high strains the diameter of a filament is often seen to become constant some distance down the spin line, which would of course imply a vanishing rate of strain. This could only happen where the structure formed has an extremely long relaxation time, rather greater than might be expected from a model based solely on entanglement orientation. Breakdown of an oriented gel complex could not only require loss of entanglement, but also a re-dissolution (the movement of eqn. (1) to the left), which is a much slower process. Experimental methods Elongational

j7ow

Experiments were carried out using the Elongational Viscometer manufactured by Sangamo Transducers Ltd based on the design of Ferguson and Hudson [14]. Ambient temperature (21°C) was used throughout.

TABLE 1 Some typical flow phenomena

observed

during elongational

flow

Polymer solution

Drum speed (m-s-‘)

Total strain at the drum

Phenomena

Silicone Oil (no =1.3 Pa-s) with Al ,O _ .1 particles

0.0

0.8

Pure extensional

flow

0.35

2.2

Pure extensional

flow

0.5% PAM in ethylene glycol(q,=1.4Pa.s) with Al 203 particles

0.0 0.35

0.8 2.2

Pure extensional flow Anomalous flow. Particles moving at different speeds dependent upon their radial position. Faster particles in the body overtaking slower ones on the outside of the filament

5% PEO in water (no = 45 Pa-s)

0.05 1.50

0.9 3.4

Tack high. Fluid adheres to syringe needle touching filament No obvious tack. Syringe needle passes through filament without fluid adhering

4.5% PEO in water (no = 31 Pa.s)

0.05

0.9

2.00

3.5

Filament deflected by air jet, returns to equilibrium when the disturbance is removed When the deflecting air jet is removed, the filament laterally. The vibrations die out slowly

0.80 2.00

1.8 3.3

2% PAA in ethylene glycol. (qc = 98 Pa-s)

observed

position oscillates

Fluid adheres to and is drawn by the rotating drum Filament bounces off drum surface. Temporary adherence followed by ligaments being thrown off the drum

is

TABLE 2 Characteristics

of solvent systems and 2.91% solutions

of atactic PMMA in the solvent PMMA

Solvent system

kg/kg (g/g)

Density kg.rn-? (g.cm-’

100/o 90/10 80/20 70/30 60/40 50/50 40/60

862.3 870.0 877.8 885.7 893.9 902.2 910.5

Toluene/Cyclohexanol

Viscosity mPa.s X 103)

(cP)

solubility parameter (MPa)“.5 x 0.4889 (caf”-s.cm-‘-5)

Density kg.rn(g.cm-s

0.55 0.62 0.75 0.95 1.29 1.85 2.72

8.90 9.13 9.36 9.61 9.85 10.10 10.35

868.7 875.1 882.0 889.5 897.6 905.5 913.2

Solution Viscosity mPa.s X103)

Specific viscosity

(cP) 1.09 1.38 1.72 2.10 2.70 3.67 4.95

0.982 1.238 1.290 1.210 1.090 0.985 0.820

60 Photography A Hadland Hyspeed rotating prism camera was used to record flow phenomena. The conditions under which particular effects were recorded are shown in Table 1. Flash photography was used to obtain still photographs. Solubility parameter Using the method described by 2.91% (w/w) solutions of actactic determined, Table 2. A Ubbelohde plotted against the known solubility was obtained which corresponded to Fig. 5.

Barton [15], the specific viscosities of PMMA in a series of solutions were viscometer was used at 21°C. When parameters of the solvents, a maximum the solubility parameter of the PMMA,

1.2 Specific

Viscosity 1. ‘IlO

Solubility

Parameter

6 /2.0455

x

k,f’a”

Fig. 5. The specific viscosity of 2.91% (w/w) solutions of atactic PMMA in various solvents (cf. Table 2), plotted against the solubility parameters of the solvents. The maximum in the curve gives a good estimate of the solubility parameter of the PMMA (9.34 X 2.046 MPa”.5).

61 TABLE

3

Solutions tested using the pendant drop method Polymer

Solvent

Concentration

Observation

% (w/w> PMMA

DMMP

5

FM9

DPM

2

PEO

Water

5

PAM

Paraffin

1.5

Drop falls, pulling a filament, then stops, and starts to rise. Droplets formed on the filament Drop falls, pulling a filament. Hits a flat surface. Droplets formed on the filament Drop falls, pulling a filament. Hits a flat surface. Droplets formed on the filament Drop falls, pulling a filament. Hits a flat surface. No droplets formed, filament retracts

Pendant drop method Various solutions, Table 3, were allowed to drop under gravity from a capillary, using a similar technique to that used by Jones and Rees [16]. Due to a liquid’s high spinnability, a filament formed between the drop and the capillary exit. This filament was elongated as the drop fell. For a 5% (w/w) solution of the PMMA (@ = 856 000) in dimethyl methane phosphonate (DMMP), the drop initiahy accelerated under gravity. However, after a short time it started to decelerate, came to rest, and then began to retract up the filament. The drop and filament were then photographed at time intervals (over the following 60 s) using flash photography. For other solutions, elongation was suddenly stopped when the drop struck a flat surface, and the filaments were then photographed using the Hyspeed Camera. A 2% (w/w) solution of FM9 (a copolymer of tertiary butyl styrene with monomers containing associating groups, of M, > 5 000 000, manufactured by ICI PLC) in dipropylene glycol monoethyl ether (DPM) was tested in this manner, and on cessation of elongation, sections of the filament, together with several of the droplets formed on the filament, were caught on microscope slides, allowed to dry in air at 2O”C, and photographed using a Wild M21 microscope system. Experimental results In order to illustrate how widespread the anomalous effects are in extending fluids, the results have been obtained for a range of polymer solutions.

62 Visualisation experiments

Results for systems of a 0.5% (w/w) solution of polyacrylamide (PAM) in ethylene glycol (EG) and silicone oil of comparable zero shear viscosity, in which Al,O, particles had been dispersed, have been reported [17]. At low strains, both systems showed a uniform extension across the radius of the filament. For the silicone oil, this situation was maintained at higher strains. However, as the strain was increased for the PAM in EG, certain particles on the outside of the filament were observed to move at different velocities to those in the body of the filament. Tack

Pronounced tack changes were observed (Table l), as rate of elongation of the fluid emerging from the elongational viscometer increased. At low extensions, a 5% (w/w) solution of polyethylene oxide (PEO) (a, =

Plate 1. The tackiness of polymer solutions. A 5% (w/w) solution of PEO in water is issuing from the Sangamo Elongational Viscometer. On the left, a syringe needle has just touched the filament, which adheres to it. On the right, the needle has been removed from the filament, but ligaments of solution still adhere.

63

Plate 2. The loss of tack under high extension. A 5% (w/w) solution of PEO in water is issuing from the Sangamo Elongational Viscometer, drum speed set at 1.5 m-s-‘. On the left, a syringe needle passes through the filament %&ut disturbing the flow. On the right, the needle has been removed from the filament and no solution has adhered to it.

4000000) in water adhered strongly to any object with which it came into contact. Plate 1 shows a syringe needle moving away from the elongating fluid, having just made contact with it. At high rates of extension, Plate 2, the needle could be pushed firmly through the filament, and then withdrawn without any fluid adhering to it. Lateral vibrations Further evidence of changes in the viscoelastic behaviour with elongation rate was observed with a 4.5% (w/w) solution of PEO in water. At a total Hencky strain of 0.9, a short blast of compressed air at right angles to the filament produced an immediate deflection which appeared heavily “damped”, returning to its equilibrium position immediately the disturbance stopped. In contrast, at a Hencky strain of 3.3, the immediate deflection produced by air was sustained when the disturbance was removed, dying out only slowly.

64 Drum adhesion

Plate 3 shows a problem well known to experimental& working with extensional viscosity. A 2% (w/ w) solution of polyacrylic acid (PAA) (M,= 4 000 000) in ethylene glycol, having a zero shear viscosity of 98 Pa - s,

Plate 3. Bouncing from the drum. A 2% (w/w) solution of PAA in ethylene glycol is issuing from the Sangamo Elongational viscometer, drum speed set at 2.0 rn. s- ‘. Whilst maintaining its circular cross section, the filament bounces off the drum in an elastic collision, before gravity starts to bend it back to the vertical. The angle of incidence and the angle of reflection are about equal (loo).

65

Plate 4. Droplet formation on an elongated filament. A drop of a 5% (w/w) solution of PMMA in DMMP has issued from a capillary and has fallen under gravity, elongating the filament attached to itself and the capillary exit. Aftrer a few seconds, the drop came to rest, and the formation of droplets was photographed: (a) 10 seconds after issue from the capillary, (b) 15 s, (c) 45 s, (d) 60 s, and (e) 60 s, a continuation of (d) at the point AB. The filament in (b) is thinner than in (a) since many more droplets have formed under surface tension, and there has been little retraction of the filament. In (c), the filament has retracted considerably and many droplets have coalesced to form larger ones. This process has continued in (d) and (e).

66 was extruded from the spinnerette. The drum speed was set at 200 cm/s. When the filament touched the drum, it was, at first, taken up in the usual manner. However, it very quickly changed its behaviour. It began to bounce off the drum, with a definite and sharp angle of deflection, very reminiscent of an elastic collision of an object with a wall. Its velocity on meeting the drum was approximately 160 cm/s. Occasionally, it attached itself to the

Plate 5. Droplet formation on an elongational filament. An enlar sgement of the point A in Plate 4. The polymer rich filament is seen to pass straight through the droplet of solvenl t rich phase.

67 drum, but was then thrown off in coherent ligaments before returning to the bouncing behaviour. The same phenomenon occurred when the drum was started from rest with the filament already falling, the bouncing effect starting at a drum speed of about 180 cm/s.

Plate 6. Droplet formation on an elongated filament. Filament and droplets from an elongated 2% (w/w) solution of FM9 copolymer in DPM have been collected on a microscope slide. The polymer rich filament is seen to pass straight through the droplets of solvent rich phase. Each division of the scale is 100 pm.

68 Droplet formation

Perhaps the most striking example of flow anomaly occun red when cert ain polymer solutions were elongated to a given length, and then elongat .ion ceased. Plate 4 shows a typical example of the phenon lenon obsen red. Droplets formed, in this case in the solution of PMMA inL DMMP. Thkese droplets grew with time, eventually coalescing and runniq g down the f‘ila-

Plate 7. Droplet formation on an elongated filament. A similar slide to that in Plat e 6, photographed at a later time. The break in the filament suggests that a redissolution of’ the polymer is taking place, that is, the reaction in eqn. (1) is moving to the left.

69 ment. It can be seen clearly at position A in Plate 4, and the magnified view shown in Plate 5, that the filament continues intact through the fluid droplet. It is also evident from this photograph that the opaque filament continues through the ligament joining the two droplets and is surrounded by clear fluid. The opacity of the filament suggests a different refractive index from the clear solution and indicates the presence of a gelled phase which has come out of solution. Solvent evaporation can be discounted as a reason for the gelling. The solvent DMMP has a very high boiling point (181°C), a correspondingly low vapour pressure (0.61 mm Hg at 2O”C), giving a negligible volatility. Further evidence is shown in Plates 6 and 7. In this case the solution was 2% FM9 copolymer in DPM. Filament and droplets were caught on a glass slide and photographed. Two points can be noted. Firstly, in many of the droplets, the filament can be seen to be passing straight through. Secondly, the concentration of polymer in the droplet would seem to be much lower than in the filament. It was also noted that, in some cases, the filament appeared to have broken in the droplet. This may be associated with a comparatively slow re-dissolution process in the droplet occurring when strain is removed from the filament. Discussion A number of flow phenomena are reported in this paper, in a number of different fluids. Many of the phenomena occurred in more than one of the fluids. For example, droplet formation has been observed in aqueous solutions of PEO, PAM in ethylene glycol, very high molecular weight polybutadiene in dekalin, and others. The phenomenon of fluid bouncing off a drum on loss of tack is similarly widespread. As was mentioned earlier, it is to give some indication of how general the flow effects are that we have given results in a range of solutions. There are two clear pieces of evidence for the existence of two phases in a high extension flow field. The first, reported in an earlier paper [17], is the observation of a non-uniform velocity profile in a highly elastic fluid as demonstrated by the flow behaviour of entrained particles. Those particles on the outside of a rapidly extending filament moved with a lower velocity to those in the body of the fluid. It was established that this could not be attributed to artefacts such as air drag or photographic distortion. Secondly, as Plates 4 and 5 show, the filament continued through the fluid droplets formed when the elongation was suddenly stopped. The growth of the droplets themselves can be attributed to the progressive effects of surface tension acting on a lower viscosity annulus of solvent rich phase surrounding the extended filament. This is confirmed by Plate 6, which shows that the

70 polymer concentration within the filament is much higher than in the droplet. The failure of the filament within some drops is discussed below. The concept of phase separation, with a polymer rich phase in the centre and a solvent rich annular phase can now be used to explain the other phenomena observed in rapid elongational flows. As is well known, most polymer solutions at rest or in a slow flow field will show a considerable degree of tack. This is a complicated phenomenon related to cohesive energy density, polymer concentration and solution rheology [18]. The loss of tack at high elongation can be explained by a fall in polymer concentration, that is, the formation of the annular solvent rich phase. Most striking was the ability of the fluid to maintain its integrity when disturbed by a syringe needle at high rates of flow. When the needle was slowly driven into the filament, fluid did not adhere to the needle. This was in contrast to the disruption which occurred at low flow rates. As Plate 3 shows, the filament in contact with the rotating drum was sharply deflected whilst maintaining a circular cross section. The drum typically rotated at a somewhat higher speed than the fluid velocity at the point of contact. Obviously the filament’s loss of tack prevented adhesion with the drum, surface fluid acting as a lubricant. Particularly striking is the fact that the angle of incidence equals the angle of reflection (loo) signifying an elastic collision. The fact that the fluid retained a circular cross section would also indicate solid-like elastic behaviour, presumably in the core of the filament. This appeared to be retained when, momentarily, adhesion occurred causing the filament to be drawn round the drum for a short distance (l/4 revolution). The fact that the filament fell away as adhesion failed suggests that the structure built up in elongation had been retained. It is tempting to speculate at this stage that other anomalous effects in elongational flow could be described in the same terms. For example, the well known behaviour of a thin stream of viscoelastic fluid such as polyisobutylene in dekalin [19], or a polymer thickened proprietary detergent [20], on bouncing out of a thin layer of its own solution, may fit the hypothesis. The maintained vibrational behaviour noted in aqueous PEO solutions, amongst many others, does not directly constitute evidence for the presence of two phases. It could be well explained in terms of long lifetime polymer entanglements [21] inducing solid-like elastic behaviour. Nevertheless, if complexation had occurred, the effect would be greatly enhanced. This now leads us back to a consideration of strain hardening. Where a highly orientated polymer complex has formed, the secondary intermolecular bonds will resist further deformation, producing an increase in elongational viscosity. This may tend to be reduced by the presence of a low viscosity solvent rich phase, however, it would appear that the net effect would be a viscosity enhancement, especially where gellation takes place.

71 The fluid which shows the greatest strain hardening, relative to its zero shear, and hence zero rate of elongation viscosity is synovial fluid [22]. This biological fluid has been shown to owe its high elasticity and spinnability to the presence of a protein-polysaccharide complex [23]. When this complex is destroyed by the addition of 6M urea, the fluid becomes much more Newtonian, elasticity falls drastically and spinnability vanishes. In other words, strain hardening no longer occurs. The thermodynamical evidence for the formation of complexes in a strong elongational flow is quite clear, as has been shown earlier. However, not every polymer solution will necessarily form a complex, although as Kabanov [9] has pointed out, at high molecular weight, providing cooperativity between macromolecules is high, even weak intermolecular forces can induce complexation. Perhaps the most interesting example of this is complex formation between isotactic and syndiotactic PMMA [8]. The solution of atactic PMMA in DMMP has formed a complex also. Whilst the molecular fit and cooperativity is not normally sufficient to bring about complexation in this solution at rest, the cooperativity has been enhanced sufficiently by orientation in the elongational flow field to cause interaction to occur. As Plates 4 and 5 show, this complex has gelled, due to differences in solubility parameters of the polymer and solvent. Based on the experimental results and the thermodynamics of the polymer solutions, it is now possible to come to the following conclusions: (1) Polymer complexation will be strongly enhanced by orientation under elongational flow, the presence of long polymer chains, and solubility parameter differences between polymer and solvent. (2) Even very weak interactions between complexing polymer chains will bring about gelation when the above factors are large. (3) Elongational viscosity increases at high strains and/or high strain rates may be due both to long term polymer entanglements and polymer complexation. Note Since submission of this paper, the rheological instruments division Sangamo-Schlumberger Ltd has been taken over by Carri-Med Ltd Dorking, England.

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