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16th April 2017
Tommi Borg visits for your meetings at Chinaplas May 16-19, 2017 - Guangzhou, PR China.

24th November 2015
New published paper "Linear viscoelastic model for different flows based on control theory", Appl. Rheol. Read more >>

7th November 2014
RheoPower 4.3 is also available as true 64-bit for heavy computations. Read more >>

20th August 2014
Tommi Borg gives an oral presentation at The International Conference on Polyolefin Characterization (ICPC) September 21-24, 2014 - Valencia, Spain. >>

30th October 2013
New RheoPower 4.2 produce accurate MWD by Multi-Record Analyze. Read more >>

The Background of RheoPower

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 [1-5].
[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.
[4] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part IV. From molecular dynamics to temperature and viscoelastic relations using control theory, J. Non-Newtonian Fluid Mech. 165 (2010) 24-31.
[5] T. Borg, E. J. Pääkkönen, Linear viscoelastic model for elongational viscosity by control theory, Rheologica Acta (October 2011), Doi: 10.1007/s00397-011-0598-2.
You can doownload papers and other information at Research Papers

You find some animations for molecular and chain dynamics, entanglement and disentanglementing at Animations

You find also selected control theory information as a background usable for viscoleasticity at Links

The practice

The operation systems for RheoPower software package are Windows XP, Vista, Windows 8 and 8.1 both 32-bit and 64-bit platforms.

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 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. Relative diameters of the statistical tube yields the correct Rheologically Effective Distribution (RED), which is converted to the MWD by melt calibration. - Click on the figure to zoom it.

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.

Main differences between the earlier principles

Maxwell model and its developments with different type relaxation times are logical to human being, unfortunately macromolecules do not behave according to our wants. For educational purposes the base model is descriptive. Relaxation time schema is artificial for molecular motions.

Practical difference is the fact that relaxation spectrum is thought to be as a fingerprint of behaviours and structure, unfortunately it is generated by indirect methods at first starting from G' and G'' measurements to get relaxation modulus G(t) and further spectrum h(t). We have proven that the measured partition of G' and G'' is not accurate although computed dynamic moduli G* is precise. Moreover with RheoPower is possible to get G' and G'' to all types of flows.

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