Xpansion Instruments - SER Principle of Operation


	Background on Extensional Rheology Extensional rheology is the science associated with flow and deformations involving the elongation, or stretching, of materials. When the true strain rate of extension (also referred to as the Hencky strain rate) is constant, simple extension is said to be a "strong flow" in the sense that it can generate a much higher degree of molecular orientation and stretching than flows in simple shear. Shown here are relative depictions of simple shear and extension deformations at an applied strain of 2 for samples of identical initial dimensions. As a consequence of the degree of molecular stretch and orientation that can be achieved, extensional flows are very sensitive to crystallinity and polymer long-chain branching, and as such can be far more descriptive with regard to polymer characterization than any other type of bulk rheological measurement. High-rate, transient extensional flow is also the dominant type of deformation in converging, squeezing, and stretching flows that occur in typical polymer processing operations. Although these types of transient extensional flow measurements have historically been difficult to perform on polymer melts, the revolutionary technology embodied in the SER Universal Testing Platform marks a true breakthrough in the field of polymer melt extensional rheology. Most notably, recent studies with the SER [ Rheol Acta (2004) 43: 624–633; Rheol Acta (2005) 44: 1–15] have revealed the important role of high-rate extensional flow behavior in polymer melt processability, fracture, and flow instabilities.
Another advantage of characterizing materials in extension is that slip is typically not an issue during an extensional flow measurement as it is with a material flow characterization in simple shear, particularly for elastomeric materials. Slip is an important consideration in simple shear since it reduces the applied shear deformation. In the presence of slip it is very difficult to deconvolute the effects of slip from the material's true physical response to a deformation without first quantifying the degree of slip.
	The SER extensional rheometer consists of paired master [A] and slave [B] windup drums housed in bearings [C] within a chassis [E] and mechanically coupled via intermeshing gears [D] as shown here in the schematic assembly view of the model SER2-A. Rotation of the drive shaft [F] results in a rotation of the affixed master drum [A] and an equal but opposite rotation of the slave drum [B] which causes the ends of the sample [H] that are secured to the drums by means of securing clamps [I] to be wound up onto the drums resulting in the sample being stretched over an unsupported length, L₀. [Click here to watch videoclips of the SER in action.] For a constant drive shaft rotation rate, Ω, the Hencky strain rate applied to the sample specimen can be expressed as:
dЄ_H/dt = 2 ΩR/L₀ where R is the radius of the equal dimension windup drums, and L₀ is the fixed, unsupported length (referred to as the "stretch zone") of the specimen sample being stretched, which is equal to the centerline distance between the master and slave drums. The material's resistance to stretch imparts a tangential force, F, on the surface of the drums which is then translated as a resultant torque, T, that can either be resolved as a driving torque on the rotating drive shaft [F] (as in the case of when the SER is accommodated on a Controlled Stress Rheometer) or as a twisting moment transmitted through the chassis to the stationary torque shaft [G] (as in the case of when the SER is mounted on a Controlled Rate Rheometer). This resultant torque, T, can easily be determined from a summation of moments about the primary axis of rotation, which yields: T = 2 (F + F_F) R where T is the resultant torque measured by the torque sensor and F_F is the frictional contribution from the bearings and intermeshing gears. With the precision bearings and gears outfitted on the SER3 unit, the frictional term is typically less than 1% of the measured torque signal and can be neglected such that the expression for the measured torque can be simplified to: T = 2 F R If there is no deviation between the nominal and actual strain rates, the instantaneous cross-sectional area, A(t), of the stretched specimen changes exponentially with time, t, for a constant Hencky strain rate experiment and can be expressed as: A(t) = A₀ exp[- (dЄ_H/dt) t] where A₀ is the initial cross-sectional area of the unstretched specimen. For a constant Hencky strain rate, the transient extensional viscosity (also referred to as the tensile stress growth function), η_E⁺(t), of the stretched sample can then be expressed as: η_E⁺(t) = F(t) / [A(t) (dЄ_H/dt)] where F(t) is the instantaneous extensional force at time t exerted by the sample as it resists stretch as determined from the measured torque signal, T. Hence, for a given rate of extensional deformation, the measured torque signal is directly related to the extensional viscosity of the specimen being stretched in the isolated "stretch zone" of length L₀ defined by the tangent plane between the drums.