Polymer chain entanglement

Cross,M. M. Viscosity, molecular weight, and chain entanglement. Polymer (London) 11,238-244 (1970). 

These expressions describe the influence of polymer molecular weight on the dissolution process. There is a similarity between concentrated polymer solutions and the amorphous solid state. As the concentration of polymer solutions increases, it can be supposed there is a greater degree of intermolecu-lar chain entanglement. Polymer chains tend to be entangled in the solid state. Obviously, the kinetics of dissolutions will be slow, even when the sign and magnitude of is favourable, since a considerable amount of chain... 

Figure C2.1.13. (a) Schematic representation of an entangled polymer melt, (b) Restriction of tire lateral motion of a particular chain by tire otlier chains. The entanglement points tliat restrict tire motion of a chain define a temporary tube along which tire chain reptates.

Next let us consider the differences in molecular architecture between polymers which exclusively display viscous flow and those which display a purely elastic response. To attribute the entire effect to molecular structure we assume the polymers are compared at the same temperature. Crosslinking between different chains is the structural feature responsible for elastic response in polymer samples. If the crosslinking is totally effective, we can regard the entire sample as one giant molecule, since the entire volume is permeated by a continuous network of chains. This result was anticipated in the discussion of the Bueche theory for chain entanglements in the last chapter, when we observed that viscosity would be infinite with entanglements if there were no slippage between chains. 

Whether the beads representing subchains are imbedded in an array of small molecules or one of other polymer chains changes the friction factor in Eq. (2.47), but otherwise makes no difference in the model. This excludes chain entanglement effects and limits applicability to M < M., the threshold molecular weight for entanglements. 

The alcohol swells the poly (ethyl methacrylate) beads, rapidly promoting diffusion of the plasticizer into the polymer. As a result of the polymer-chain entanglement, a gel is formed. The conditioner is applied to the denture and provides a cushioning effect alcohol and plasticizer are slowly leached out, and the material becomes rigid. To ensure resiliency, the conditioner must be replaced after a few days. Some materials exhibit high flow over a short period compared with others with low initial flow the latter remain active longer. 

The melt viscosity of a polymer at a given temperature is a measure of the rate at which chains can move relative to each other. This will be controlled by the ease of rotation about the backbone bonds, i.e. the chain flexibility, and on the degree of entanglement. Because of their low chain flexibility, polymers such as polytetrafluoroethylene, the aromatic polyimides, the aromatic polycarbonates and to a less extent poly(vinyl chloride) and poly(methyl methacrylate) are highly viscous in their melting range as compared with polyethylene and polystyrene. 

Amorphous stereotactic polymers can crystallise, in which condition neighbouring chains are parallel. Because of the unavoidable chain entanglement in the amorphous state, only modest alignment of amorphous polymer chains is usually feasible, and moreover complete crystallisation is impossible under most circumstances, and thus many polymers are semi-crystalline. It is this feature, semicrystallinity, which distinguished polymers most sharply from other kinds of materials. Crystallisation can be from solution or from the melt, to form spherulites, or alternatively (as in a rubber or in high-strength fibres) it can be induced by mechanical means. This last is another crucial difference between polymers and other materials. Unit cells in crystals are much smaller than polymer chain lengths, which leads to a unique structural feature which is further discussed below. 

Langley, N.R. and Polmanteer, K.E., Role of chain entanglements in rubber elasticity. Polym. Prep. Am. Chem. Soc. Div. Polym. Chem., 13(1), 235-240 (1972). 

M. Cates. Reptation of living polymers Dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 20 2289-2296, 1987. 

The rigid chemical structure of a conjugated polymer helps in the movement of electrons. That stiff structure, however, has limited its use. They are like uncooked spaghetti and do not easily entangle themselves. Polymer chain entanglements are necessary to achieve high viscosities, which are required to create fibers out of these polymers. 

The solidity of gel electrolytes results from chain entanglements. At high temperatures they flow like liquids, but on cooling they show a small increase in the shear modulus at temperatures well above T. This is the liquid-to-rubber transition. The values of shear modulus and viscosity for rubbery solids are considerably lower than those for glass forming liquids at an equivalent structural relaxation time. The local or microscopic viscosity relaxation time of the rubbery material, which is reflected in the 7], obeys a VTF equation with a pre-exponential factor equivalent to that for small-molecule liquids. Above the liquid-to-rubber transition, the VTF equation is also obeyed but the pre-exponential term for viscosity is much larger than is typical for small-molecule liquids and is dependent on the polymer molecular weight. 

Due to dieir compact, branched structure and to die resulting lack of chain entanglement, dendritic polymers exhibit much lower melt and solution viscosity dian their lineal" counterparts. Low a-values in die Mark-Houwink-Sakurada intrinsic viscosity-molar mass equation have been reported for hyperbranched polyesters.198 199 Dendrimers do not obey diis equation, a maximum being observed in die corresponding log-log viscosity-molar mass curves.200 The lack of chain entanglements, which are responsible for most of the polymer mechanical properties, also explains why hyperbranched polymers cannot be used as diermoplastics for structural applications. Aldiough some crystalline or liquid... 

The remaining problem in the model development is to estimate the decrease in kp as a function of conversion. As the reaction proceeds beyond the point of chain entanglement, a critical conversion is reached where the propagation reaction becomes diffusion controlled and kp begins to fall with further increase in polymer concentration. At the critical conversion, one may write... 

The overall result is that in the melt the polymer molecules adopt Gaussian configurations and behave as thermodynamically ideal entities. This combination of ideality and chain entanglement has been confirmed by neutron scattering experiments and is well established despite the apparent paradox. 

The interconnection between the two different polymers can cause some essentially thermoplastic polymers to behave as thermosets when combined in an IPN. This arises because of chain entanglement between different polymers. The entanglements behave as crosslinks at lower temperatures but they can be broken by heat. 

Tsui, O. K. C. and Zhang, H. F. (2001) Effects of chain ends and chain entanglement on the glass transition temperature of polymer thin films. Macromolecules, 34, 9139—9142. 

Sato, N., Ito, S. and Yamamoto, M. (1998) Molecular weight dependence of shear viscosity of a polymer monolayer evidence for the lack of chain entanglement in the two-dimensional plane. Macromolecules, 31, 2673-2675. 

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