
The Background of RheoPower
The principleThe analytical model is based on Control Theory of dynamic systems and fast characteristic model gives simple equations for a dynamic system.New Rheologically Effective Distribution (RED) function gives the relation between time, frequency and shear rateand the molecular weight scales. Further developed melt calibration has similarities with the widely used universal calibration. Formulas join viscosity, relaxation modulus and other flow properties with polymer structure.
The main featuresViscoelastic properties are modelled by the Rheologically Effective Distribution (RED) related to the material structure. MWD and RED are converted from each other by melt calibation.The best proof of the principle is the computation results, although the complete theory is published [16]. [1] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part I. Relaxation modulus and melt calibration, J. NonNewtonian 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. NonNewtonian Fluid Mech. 156 (2009) 129–138.[3] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part III. Startup and transient flow effects from the molecular weight distribution, J. NonNewtonian Fluid Mech. 159 (2009) 1725.[4] T. Borg, E. J. Pääkkönen, Linear viscoelastic models: Part IV. From molecular dynamics to temperature and viscoelastic relations using control theory, J. NonNewtonian Fluid Mech. 165 (2010) 2431.[5] T. Borg, E. J. Pääkkönen, Linear viscoelastic model for elongational viscosity by control theory, Rheologica Acta (October 2011), Doi: 10.1007/s0039701105982.[6] Borg, E. J. Pääkkönen, Linear viscoelastic model for different flows based on control theory, Appl. Rheol. 25 (2015) 64304.You can doownload papers and other information at Research Papers You find some animations for molecular and chain dynamics, entanglement and disentanglementing at the page Animations of the principle at molar level. You find also selected control theory information as a background usable for viscoleasticity at Links
The practiceThe operation systems for RheoPower software package are working only on Windows 7, 8 and 8.1, Vista and 10 platforms and only on 64bit.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 MWDTentative 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 backgroundModern 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 CoxMerz rulesPower law is explained on our published manuscripts, Part III.The original CoxMerz 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 CoxMerz 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 CoxMerz 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 “ultracorrelation” between different flows and MWD looks unbelievable, you obtain a wrap up as follows:
Main differences between the earlier principlesMaxwell 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. 