Preface

**Section 3 Suspensions, Colloids and Granular Materials 133**

Chapter 8 **Rheology of Highly Filled Polymers 153**

Clemens Holzer

**VI** Contents

Chapter 7 **Interparticle Interaction Effects in Polymer Suspensions 135**

Nico Laufer, Harald Hansmann, Christian Boss and Stefan Ofe

Christian Kukla, Ivica Duretek, Joamin Gonzalez-Gutierrez and

Rheology is the science that studies the flow behavior of materials, whether in a solid or liquid state, under the application of a stress or deformation to obtain a response to an applied force.

Rheology has some wide application areas that include foods, textiles, personal care products, pharmaceuticals, and polymers, among others. In polymers, rheology has become an impor‐ tant tool to understand the behavior of polymers under processing conditions, and to help to design equipment such as injectors, extruders, and other polymer processing equipment.

In diluted suspension applications and colloidal dispersions, rheological behavior is a rele‐ vant topic mainly in concentrated materials because of its high theoretical and experimental complexity. Research work in this field is of high industrial importance especially in the de‐ sign, production, and shipping phases.

Also, mathematical modeling in research work has been developed in a particular way so that the modeling of complex phenomena such as thixotropy or thinning generates an inter‐ est for a variety of problems.

Special studies in materials rheology, where it depends on the nature of the stimulus to which it responds, are those that show magnetorheological and electrorheological properties (depending on magnetics or electrical fields). These materials are created by permeable sus‐ pended particles in a medium that is either magnetic or conducting according to the case, and react to external stimuli by returning to their initial conditions. They recover their origi‐ nal property, repeating this process many times without deterioration; therefore, they are defined as "intelligent fluids."

Another area of application of rheology in polymers is to help understand the structure–prop‐ erty relationship by means of changes in molecular weight, molecular weight distribution, morphology, melt degradation, and performance under processing conditions, among others.

There are several ways to evaluate rheological behavior, but mainly it is assessed to obtain rheological curves, which can be carried out in rotational, oscillatory, or creep mode.

The present book is divided into three sections: "Advances in new rheology applications," "Polymers and biopolymers rheology," and "Suspensions, colloids and granular materials rheology," covering several application areas, interpretation of results, mathematical mod‐ els, as well as determining other areas where rheology and rheological phenomena can be understood.

The first section presents work that can be regarded as a novelty, mainly trying to explain phenomena that are not often reported in rheology, in addition to developing new materi‐ als. The second section focuses on works concerning the rheology of polymers and biopoly‐ mers, which can have applications for petroleum recovery, as well as applications in biochemistry. The last section shows work that explains changes in the rheological behavior of materials having suspensions, colloids, or particles in a polymer.

This book comprises research work that tries to help the reader to understand the science of rheology, presenting novel work in the polymer rheology area.

> **Dr. José Luis Rivera-Armenta and Dr. Beatriz Adriana Salazar-Cruz** National Technologic of Mexico (TecNM) Technological Institute of Madero City, Mexico

**Section 1**

**Advances in New Rheology Applications**

**Advances in New Rheology Applications**

mers, which can have applications for petroleum recovery, as well as applications in biochemistry. The last section shows work that explains changes in the rheological behavior

This book comprises research work that tries to help the reader to understand the science of

**Dr. José Luis Rivera-Armenta and Dr. Beatriz Adriana Salazar-Cruz**

National Technologic of Mexico (TecNM) Technological Institute of Madero City, Mexico

of materials having suspensions, colloids, or particles in a polymer.

rheology, presenting novel work in the polymer rheology area.

VIII Preface

**Chapter 1**

Provisional chapter

**Magnetorheology of Polymer Systems**

The results of researches of a magnetic field effect on rheological properties of both paramagnetic, and diamagnetic polymer systems are described. Influence of intensity and the direction of power lines of the magnetic field on the viscosity of magnetic liquids and magnetorheological suspensions is analyzed. Results of theoretical researches of the magnetic field effect on the diamagnetic macromolecule orientation in solutions are discussed. The data on the influence of the magnetic field on rheological parameters of cellulose ether solutions are generalized and analyzed. The rheological parameters are compared with a change of studied system structure under magnetic field. The concentration dependences of viscosity and the sizes of supramolecular particles in solutions are compared. The rheological behavior of systems in a region of phase transitions is considered. Concentration dependences of the viscosity are described by curves with a maxi-

DOI: 10.5772/intechopen.75768

There are two classes of substances with various magnetic properties; paramagnetics and diamagnetics. Paramagnetic placed in a magnetic field with an intensity of H is magnetized in the direction coinciding with the direction of power lines of the field. Thus, a magnetic moment μ arises in a sample. The paramagnetism is caused by the orientation of the magnetic moments of atoms and molecules of the paramagnetic under the field. At the same time μ = χparН, where χpar is a paramagnetic susceptibility, χpar>>0. The paramagnetic particles distributed in the liquids are oriented along the force lines of the external field that leads to an

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

aggregation of particles and to a viscosity growth of such systems (magnetic liquids).

mum which concentration corresponds to a phase transition concentration.

Keywords: polymer systems, magnetic field, rheology, structure

Magnetorheology of Polymer Systems

Sergey Vshivkov and Elena Rusinova

Sergey Vshivkov and Elena Rusinova

http://dx.doi.org/10.5772/intechopen.75768

Abstract

1. Introduction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Magnetorheology of Polymer Systems** Magnetorheology of Polymer Systems

#### Sergey Vshivkov and Elena Rusinova Sergey Vshivkov and Elena Rusinova

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75768

#### Abstract

The results of researches of a magnetic field effect on rheological properties of both paramagnetic, and diamagnetic polymer systems are described. Influence of intensity and the direction of power lines of the magnetic field on the viscosity of magnetic liquids and magnetorheological suspensions is analyzed. Results of theoretical researches of the magnetic field effect on the diamagnetic macromolecule orientation in solutions are discussed. The data on the influence of the magnetic field on rheological parameters of cellulose ether solutions are generalized and analyzed. The rheological parameters are compared with a change of studied system structure under magnetic field. The concentration dependences of viscosity and the sizes of supramolecular particles in solutions are compared. The rheological behavior of systems in a region of phase transitions is considered. Concentration dependences of the viscosity are described by curves with a maximum which concentration corresponds to a phase transition concentration.

DOI: 10.5772/intechopen.75768

Keywords: polymer systems, magnetic field, rheology, structure

#### 1. Introduction

There are two classes of substances with various magnetic properties; paramagnetics and diamagnetics. Paramagnetic placed in a magnetic field with an intensity of H is magnetized in the direction coinciding with the direction of power lines of the field. Thus, a magnetic moment μ arises in a sample. The paramagnetism is caused by the orientation of the magnetic moments of atoms and molecules of the paramagnetic under the field. At the same time μ = χparН, where χpar is a paramagnetic susceptibility, χpar>>0. The paramagnetic particles distributed in the liquids are oriented along the force lines of the external field that leads to an aggregation of particles and to a viscosity growth of such systems (magnetic liquids).

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An increase in the viscosity of magnetic liquids under application of a magnetic field (the magnetorheological effect [1]) was discovered experimentally in the 1950s [2] for the systems based on iron carbonyl and iron oxide. Subsequently, this phenomenon was studied in some reports [3–15]. It was found that, in resting compositions, a structure formation is observed as a result of the magnetodipole interaction of particles and orientation of anisodiametrical structural elements along magnetic force lines. As the shear rate increases, the aggregates break up. Each combination of the given parameters (the viscosity of dispersion medium, the magnetic properties of particles, the field strength, and the shear rate) is characterized by a certain set of structural elements and their mutual disposition. An important feature of the rheological properties of ferrofluids in the magnetic field is their dependence on the mutual orientation of shear and magnetic field. An increment of the effective viscosity of a medium at the perpendicular orientation substantially exceeds the effective viscosity induced by a parallel field. A strong anisotropy of rheological properties upon field orientation along the flow rate, along its gradient, and along the direction of its vortex was revealed in [15]. The new experimentally observed phenomena for ferrofluids are the Weissenberg effect [16], which was detected earlier only in polymer and liquid crystalline media, and the shear-induced reduction in the degree of anisotropy of the internal structure of ferrofluids, as was revealed by smallangle neutron scattering [17]. The effect of magnetic field and surfactants on the rheological properties of strontium ferrite suspensions was studied in [18]. It was shown that, under application of the field, the viscosity of the suspension increases. This phenomenon was explained by the formation of three-dimensional chain structures from the ferrite particles. After the field is switched off, these structures do not decompose fully, and this circumstance is responsible for the hysteresis of suspension viscosity. After introduction of polyelectrolytes into a suspension, its viscosity decreases both in the field and after its switching off. This is caused by a decrease in the interparticle friction and weakening of the strength of threedimensional structures owing to the formation of a double electrical layer on the surface of particles. In [19], the magnetoviscous properties of two types of magnetic fluids based on iron oxide Fe3O4 were compared: the first one included oleic acid as a surfactant, and in the second one, the surfactant was tetramethylammonium hydroxide. It was shown that the type of surfactant strongly affects the fluid behavior in the magnetic field: in the presence of oleic acid, a change in viscosity under application of the magnetic field occurs more rapidly than that in the presence of tetramethylammonium hydroxide. The rheological properties of magnetic fluids ferroparticles-poly(α-olefins)-polyurethane, ferroparticles-n-octyl-pyrrolidone-butyl acrylate, and ferroparticles-n-octylpyrrolidone-pentafluorostyrene were studied in [20]. Recent advances in the field of magnetic fluids were highlighted in reviews [1, 21–26].

absence, respectively) is described by a curve with a maximum. This is explained by the transition from chain aggregates of nanoparticles to drop-shaped ones. The magnetic field with force lines oriented perpendicularly to the rotor rotation axis increases the viscosity of systems to a much higher extent than upon parallel orientation. However the data on magnetorheological properties of the paramagnetic systems containing polymers are not

Diamagnetism is an appearance in substance of a magnetic moment directed toward to the external field, at the same time χdiam<<0. Molecules (atoms) of diamagnetic substances have not any unpaired electrons. The theoretical and experimental investigations of interaction of diamagnetic macromolecules with a magnetic field are currently under development [30–64]. It was found experimentally that application of a magnetic field leads to an orientation of macromolecules and their associates along the force lines, to the increase in phase transition

If an anisotropic macromolecule is placed in a magnetic field, then a force acts on it and causes its rotation. The magnetic anisotropy of chemical bonds is responsible for the magnetic anisotropy of the molecule. In polymer systems, the amount of contacts between macromolecules is high; therefore, an orientation of polymer chains proceeds cooperatively. The effect of the field consists in the rotation (orientation) of macromolecular domains in a certain predominant direction that depends on the sign of diamagnetic susceptibility anisotropy Δχ<sup>M</sup> for this polymer. Domains are taken to mean the anisotropic associates of macromolecules or mesophase regions. The diamagnetic moment appearing at the domain under magnetic field

where V is domain volume, μ<sup>0</sup> is a magnetic constant of vacuum, B is a vector of magnetic

Interaction of external magnetic field with the domain having the magnetic moment μ

<sup>⊥</sup> diamagnetic susceptibility in the direction perpendicular to domain axis. Magnetic orientation is observed when Emag exceeds the value of thermal energy (kBT), kB is the Boltzmann's constant, T represents the absolute temperature. From here it follows [31]:

This equation determines the minimal critical volume capable to orientation.

The rotational moment of the domain (N) is expressed as [35]:

induction, ξ is an angle between the direction B and the domain axis.

increases energy of magnetic field by value of Emag [31]:

ð1Þ

Magnetorheology of Polymer Systems http://dx.doi.org/10.5772/intechopen.75768 5

ð2Þ

ð3Þ

temperatures, causes a formation of domains in solutions.

numerous [20, 29].

can be written as [32, 34]:

where χ <sup>M</sup>

To understand the internal physical nature of the magnetoviscous effect, new data on the effect of magnetic field and deforming flow on the dynamics of these systems are required. For example, up to now, the data on the effect of concentration of a magnetic fluid and the rate of its deformation on the magnetorheological effect have been scarce. Papers [24, 25, 27, 28] deal with the concentration dependence of the effect of a constant magnetic field on the viscosity of aqueous and water-glycerol magnetic fluids based on iron and iron oxide nanoparticles. It was shown that the magnetic field enhances the fluid viscosity by 20–80 times. The concentration dependence of the relative viscosity η/η<sup>0</sup> (η and η<sup>0</sup> are the viscosities in the field and in its absence, respectively) is described by a curve with a maximum. This is explained by the transition from chain aggregates of nanoparticles to drop-shaped ones. The magnetic field with force lines oriented perpendicularly to the rotor rotation axis increases the viscosity of systems to a much higher extent than upon parallel orientation. However the data on magnetorheological properties of the paramagnetic systems containing polymers are not numerous [20, 29].

An increase in the viscosity of magnetic liquids under application of a magnetic field (the magnetorheological effect [1]) was discovered experimentally in the 1950s [2] for the systems based on iron carbonyl and iron oxide. Subsequently, this phenomenon was studied in some reports [3–15]. It was found that, in resting compositions, a structure formation is observed as a result of the magnetodipole interaction of particles and orientation of anisodiametrical structural elements along magnetic force lines. As the shear rate increases, the aggregates break up. Each combination of the given parameters (the viscosity of dispersion medium, the magnetic properties of particles, the field strength, and the shear rate) is characterized by a certain set of structural elements and their mutual disposition. An important feature of the rheological properties of ferrofluids in the magnetic field is their dependence on the mutual orientation of shear and magnetic field. An increment of the effective viscosity of a medium at the perpendicular orientation substantially exceeds the effective viscosity induced by a parallel field. A strong anisotropy of rheological properties upon field orientation along the flow rate, along its gradient, and along the direction of its vortex was revealed in [15]. The new experimentally observed phenomena for ferrofluids are the Weissenberg effect [16], which was detected earlier only in polymer and liquid crystalline media, and the shear-induced reduction in the degree of anisotropy of the internal structure of ferrofluids, as was revealed by smallangle neutron scattering [17]. The effect of magnetic field and surfactants on the rheological properties of strontium ferrite suspensions was studied in [18]. It was shown that, under application of the field, the viscosity of the suspension increases. This phenomenon was explained by the formation of three-dimensional chain structures from the ferrite particles. After the field is switched off, these structures do not decompose fully, and this circumstance is responsible for the hysteresis of suspension viscosity. After introduction of polyelectrolytes into a suspension, its viscosity decreases both in the field and after its switching off. This is caused by a decrease in the interparticle friction and weakening of the strength of threedimensional structures owing to the formation of a double electrical layer on the surface of particles. In [19], the magnetoviscous properties of two types of magnetic fluids based on iron oxide Fe3O4 were compared: the first one included oleic acid as a surfactant, and in the second one, the surfactant was tetramethylammonium hydroxide. It was shown that the type of surfactant strongly affects the fluid behavior in the magnetic field: in the presence of oleic acid, a change in viscosity under application of the magnetic field occurs more rapidly than that in the presence of tetramethylammonium hydroxide. The rheological properties of magnetic fluids ferroparticles-poly(α-olefins)-polyurethane, ferroparticles-n-octyl-pyrrolidone-butyl acrylate, and ferroparticles-n-octylpyrrolidone-pentafluorostyrene were studied in [20]. Recent

4 Polymer Rheology

advances in the field of magnetic fluids were highlighted in reviews [1, 21–26].

To understand the internal physical nature of the magnetoviscous effect, new data on the effect of magnetic field and deforming flow on the dynamics of these systems are required. For example, up to now, the data on the effect of concentration of a magnetic fluid and the rate of its deformation on the magnetorheological effect have been scarce. Papers [24, 25, 27, 28] deal with the concentration dependence of the effect of a constant magnetic field on the viscosity of aqueous and water-glycerol magnetic fluids based on iron and iron oxide nanoparticles. It was shown that the magnetic field enhances the fluid viscosity by 20–80 times. The concentration dependence of the relative viscosity η/η<sup>0</sup> (η and η<sup>0</sup> are the viscosities in the field and in its Diamagnetism is an appearance in substance of a magnetic moment directed toward to the external field, at the same time χdiam<<0. Molecules (atoms) of diamagnetic substances have not any unpaired electrons. The theoretical and experimental investigations of interaction of diamagnetic macromolecules with a magnetic field are currently under development [30–64]. It was found experimentally that application of a magnetic field leads to an orientation of macromolecules and their associates along the force lines, to the increase in phase transition temperatures, causes a formation of domains in solutions.

If an anisotropic macromolecule is placed in a magnetic field, then a force acts on it and causes its rotation. The magnetic anisotropy of chemical bonds is responsible for the magnetic anisotropy of the molecule. In polymer systems, the amount of contacts between macromolecules is high; therefore, an orientation of polymer chains proceeds cooperatively. The effect of the field consists in the rotation (orientation) of macromolecular domains in a certain predominant direction that depends on the sign of diamagnetic susceptibility anisotropy Δχ<sup>M</sup> for this polymer. Domains are taken to mean the anisotropic associates of macromolecules or mesophase regions. The diamagnetic moment appearing at the domain under magnetic field can be written as [32, 34]:

$$
\mu = \frac{\Delta \chi^{\rm M}}{2\mu\_0} B^2 V \sin 2\xi \tag{1}
$$

where V is domain volume, μ<sup>0</sup> is a magnetic constant of vacuum, B is a vector of magnetic induction, ξ is an angle between the direction B and the domain axis.

Interaction of external magnetic field with the domain having the magnetic moment μ increases energy of magnetic field by value of Emag [31]:

$$E\_{mag} = - \left(\frac{1}{2}\right) V \chi\_{\perp}^{\mathcal{M}} \mu\_0^{-1} \mathcal{B}^2 - \left(\frac{1}{2}\right) V \Delta \chi^{\mathcal{M}} \mu\_0^{-1} \mathcal{B}^2 \cos^2 \xi \tag{2}$$

where χ <sup>M</sup> <sup>⊥</sup> diamagnetic susceptibility in the direction perpendicular to domain axis.

Magnetic orientation is observed when Emag exceeds the value of thermal energy (kBT), kB is the Boltzmann's constant, T represents the absolute temperature. From here it follows [31]:

$$V > \frac{2k\_B \tau \mu\_0}{|\Delta \mathcal{X}^{\mathcal{M}}|^{B^2}}\tag{3}$$

This equation determines the minimal critical volume capable to orientation.

The rotational moment of the domain (N) is expressed as [35]:

$$N = V \Delta \chi^{\mathcal{M}} \,\mu\_0^{-1} B^2 \sin \xi \cos \xi \,\omega \tag{4}$$

<sup>М</sup><sup>n</sup> = 400 and PDMS with M<sup>η</sup> = 3.4 � 104 were used. The suspensions were prepared by mixing of PEG and PDMS with aerosil nanoparticles (systems 1 and 2, respectively). The concentrations of aerosil were 4.2 and 2.0 wt% in systems 1 and 2, respectively. The magnetic fluids have

Hydroxypropyl cellulose samples with <sup>M</sup><sup>w</sup> = 1 � 105 and a degree of substitution of <sup>α</sup> = 3.2 (HPC1), with <sup>M</sup><sup>w</sup> = 1.6 � 105 and <sup>α</sup> = 3.6 (HPC2), ethyl cellulose (EC) sample with <sup>М</sup><sup>η</sup> = 2.6 � 104 and α = 2.6 have been investigated. Dimethylformamide (DMF), dimethyl sulfoxide (DMSO), ethanol and ethylene glycol were used as solvents. The purities of the solvents were confirmed by their refractive indexes. Polymer solutions were prepared in sealed ampoules for several weeks at 368 K (in DMSO), 333 K (in ethanol), 353 K (in DMF) and 363 K (in ethylene glycol). The phase state of solutions was estimated with the use of an OLYMPUS BX-51 polarization microscope. The radii of supramolecular particles, r, in moderately concentrated and concentrated solutions were determined via the method of the turbidity spectrum, which was suggested by Heller et al. [77–79] and developed by Klenin et al. [80]. Optical density А of solutions was measured with Helios spectrophotometers. The said method is based on the

composite function that depends on the relative refractive index of a solution, mrel, and

<sup>n</sup> <sup>¼</sup> <sup>d</sup>ln<sup>A</sup>

For every solution, relationships lnA versus lnλ were plotted, and the value of n was calculated from the slope of the straight line. The relative refractive index was calculated through the equation mrel = nD pol/nD sol, where nD pol and nD sol are the refractive indexes of a polymer and solvent, respectively. With the use of the tabulated data from [80], parameter α was determined for the found values of mrel and n. Parameter α is related to average weighed radius rw

> <sup>α</sup> <sup>¼</sup> <sup>2</sup>πrw λav

In this expression, the wavelength of light passing through a solution is λav = λav/nD sol, where λav is the wavelength of light in vacuum corresponding to the midpoint of the linear portion of

Solution viscosities under a magnetic field and in its absence were measured on a Rheotest RN

Rheometer was equipped with a coaxial-cylindrical operating unit made of a poorly magnetic substance, brass. Two magnets were used: the first producing a magnetic field with an intensity of 3.7 kOe and lines of force perpendicular to the rotor-rotation axis and the second one producing a magnetic field with an intensity of 3.6 kOe and lines of force parallel to the rotor-rotation axis. A metallic rotor rotating in a magnetic field can be considered as a current generator closed upon itself [81].The working generator produces

, where λ is the wavelength of light passing through a solution and n is a

<sup>d</sup>ln<sup>λ</sup> (5)

Magnetorheology of Polymer Systems http://dx.doi.org/10.5772/intechopen.75768 7

(6)

been produced by addition of iron nanoparticles to basic suspensions.

coefficient α related to dimensions of light-scattering particles:

of scattering particles via the expression:

4.1 rheometer modified by us (Figure 1).

Angstrom eq A ~ λ�<sup>n</sup>

the lnA–lnλ plot.

ω is normal vector to B and domain axis.

Therefore, it is necessary for the orientation of a diamagnetic particle to satisfy the following conditions: a particle must be anisodiametric; the particle volume must be higher than the corresponding critical value Vcr; and the medium must be low-viscosity. The particles can also be microfibers, crystallites, liquid crystals and other heterogeneous particles suspended in a liquid medium.

In the 1960s, the effect of a magnetic field on liquid crystals was theoretically studied by de Gennes and Meuer [65, 66]. It was shown that, at the critical magnetic field strength, the complete transition of a cholesteric liquid crystal to a nematic one is realized. Experimentally, this was confirmed for liquid crystals of rigid-chain polymer poly(γ-benzyl-L-glutamate) in a number of solvents in the 1970s [67, 68]. This phenomenon was explained by the orientation of liquid crystal molecules relative to force lines of the magnetic field.

Since 2006, researchers of the Chair of Macromolecular Compounds, Ural State University (since 2011 Ural Federal University), have been involved in systematic investigations of the effect of magnetic field on the phase transitions, structure, and rheological properties of liquid crystalline solutions of cellulose ethers. It was found [57–64] that application of a magnetic field leads to a change in the type of liquid crystals from cholesteric to nematic, causes formation of domains in solutions, and entails a substantial (by tens of degrees) increase in the temperature of formation of liquid crystalline phases. As the molecular mass of a polymer is increased, the ability of its molecules to orientate in the magnetic field is reduced. The solutions of cellulose ethers represent memory systems: after termination of magnetic field exposure, the orientation of macromolecules and the increased phase-transition temperature are preserved for many hours. The magnetic field leads to an increase in the sizes of associates of rigid-chain macromolecules and in the viscosity of solutions.

It should be noted that up to now there is only one theoretical [69] and some experimental works [70–76] in which an influence of the magnetic field on rheological properties of polymer solutions is considered. Note that practically no information is available on the relaxation character of the rheological behavior of polymer solutions in the magnetic field.

Therefore, the main aim of this study is to investigate the magnetorheological properties of paramagnetic and diamagnetic polymer systems
