The principle

The analytical model is based on Control Theory of dynamic systems and fast characteristic model gives simple equations for a dynamic system.

New melt calibration gives the relation between time, frequency and shear rate and the molecular weight scales. This procedure has similarities with the widely used universal calibration.

Formulas join viscosity, relaxation modulus and other flow properties with polymer structure.

The main features

Viscoelastic properties are modelled by the distributions related to the material structure.
MWD and Rheologically Effective Distribution (RED) are converted from each other by melt calibation.
The basic criterion mentioned above gives the procedure, by which appraisal of the molar mass distribution and flow structure from rheological measurements can be achieved. The best proof of the principle is the computation results, although the complete theory is published [1-3].

[1] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part I. Relaxation modulus and melt calibration, J. Non-Newtonian Fluid Mech. 156 (2009) 121–128.

[2] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part II. Recovery of the molecular weight distribution using viscosity data, J. Non-Newtonian Fluid Mech. 156 (2009) 129–138.

[3] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part III. Start-up and transient flow effects from the molecular weight distribution, J. Non-Newtonian Fluid Mech. 159 (2009) 17-25.

You can doownload papers and other information at Research Papers
You find also selected control theory information as a background usable for viscoleasticity at Links

The practice

The platform used is Windows 95/98 up to Vista.
Whilst the underlying principle is simple, the use of the numerically sensitive and labile recursive exponent formulas require accurate data together with fluent software to achieve high computing accuracy.
Also datafiles can be used by DataPower Server.

Technical Roadmap for Detecting MWD

Tentative roadmap of main lines is shown for detecting MWD.

Tentative roadmap of main lines is shown for detecting MWD. Developments of technology, presented theories at conference papers or journals and commercial software packages are sketched on the figure. Many good studies are not mentioned due to space available in the roadmap. - Click on the figure to zoom it.

Technical background

Modern principles and tools are used in numerical computation to maintain reasonable computation times. Software is applicable for the use of complex viscosity, shear viscosity, dynamic moduli and relaxation modulus, or extension, temperature and other time depend models.

Graphical demonstration of the system by Control Theory and nanostructure model of polymer melt. The stress in the molecules decreases during relaxation in distribution w(log t), and the multiplication product must be negative. The response at time t1 is defined by area A(t₁), which is scaled by factor P' to obtain the system response as a normalized relaxation function log(G(t)/G₀). Precise modeling of system response G(t) for the system input based on feedback information P' yields the correct Rheologically Effective Distribution (RED), which is converted to the MWD by melt calibration.

Power law and Cox-Merz rules

Power law is explained on our published manuscripts, Part III.

The original Cox-Merz rule and its extended or modified variations can be explained using the presented principle. Different flow scales of time frequency and shear rate do not have direct physical interrelations. Sometimes Cox-Merz rules hold and sometimes they fail completely, and this has been investigated by many studies. It is not always possible to find the correct MWD from control theory, but only on very rarely occasions has the viscoelastic properties not been modelled accurately.

Using the presented method of melt calibration yields the MWD that remains the same for different flows and scales. Thicker lines are measured data. The original Cox-Merz rule holds if P', P'' and the zero states are the same. - Click on the figure to zoom it.

Why it can be modelled so accurately?

As shown “ultra-correlation” between different flows and MWD looks unbelievable, you obtain a wrap up as follows:

• We use according to control theory reduced model principles for all molecular dynamics.
• The rheologically effective distribution (RED), w(t) and impulse response h(t) as a function of logarithmic variable log t models well viscoelastic flows by logarithmic convolution. RED is found by feedback control, deriving and fitting procedures.
• RED is converted by melt calibration to the real polymer structure and MWD.
• All procedures and formulas are linear giving strong mathematical and computational tools.