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| {{Infobox chemical analysis
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| | name = Dynamic mechanical analysis
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| | acronym = DMA
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| | classification =[[Thermal analysis]]
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| | analytes =
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| | related = [[Isothermal titration calorimetry]]<br>Dynamic mechanical analysis<br>[[Thermomechanical analysis]]<br>[[Thermogravimetric analysis]]<br>[[Differential thermal analysis]]<br>[[Dielectric thermal analysis]]
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| | hyphenated =
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| }}
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| '''Dynamic mechanical analysis''' (abbreviated '''DMA''', also known as '''dynamic mechanical spectroscopy''') is a technique used to study and characterize materials. It is most useful for studying the [[viscoelastic]] behavior of [[polymers]]. A [[sinusoidal]] [[stress (mechanics)|stress]] is applied and the [[strain (mechanics)|strain]] in the material is measured, allowing one to determine the [[complex modulus]]. The [[temperature]] of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this approach can be used to locate the [[glass transition temperature]] of the material, as well as to identify transitions corresponding to other molecular motions.
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| ==Theory==
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| ===Viscoelastic properties of materials===
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| [[Image:Dynamic+Tests+Setup+Chem+538.jpg|thumb|325px|Figure 1. A typical DMA tester with grips to hold sample and environmental chamber to provide different temperature conditions. A sample is mounted on the grips and the environmental chamber can slide over to enclose the sample.]]
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| Polymers composed of long molecular chains have unique viscoelastic properties, which combine the characteristics of [[Elasticity (physics)|elastic solid]]s and [[Newtonian fluid]]s. The classical theory of elasticity describes the mechanical properties of elastic solid where stress is proportional to strain in small deformations. Such response of stress is independent of [[strain rate]]. The classical theory of hydrodynamics describes the properties of viscous fluid, for which the response of stress is dependent on strain rate.<ref name="Ferry1980">{{cite book|last=Ferry|first=J.D.|title=Viscoelastic properties of polymers|publisher=Wiley|year=1980|edition=3}}</ref> This solidlike and liquidlike behavior of polymer can be modeled mechanically with combinations of springs and dashpots.<ref name="Ferry1991">{{cite journal|last=Ferry|first=J.D|year=1991|title=Some reflections on the early development of polymer dynamics: Viscoelasticity, dielectric dispersion and self-diffusion|doi=10.1021/ma00019a001|journal=Macromolecules|volume=24|issue=19|pages=5237–5245|bibcode = 1991MaMol..24.5237F }}</ref>
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| ===Dynamic moduli of polymers===
| | If you have a pair of Nike Free shoes, you can run freely and well.<br>In 2012, Nike Company produces new running shoes of Nike Free Run+3, Nike Free 4.0 and Nike Free 3.0 V4. The release of these shoes is held in an art garden of Sanlitun in Beijing. The technique of Nike Free can restore the natural motion of our feet and imitate the practice of bared feet.<br>It can improve our feet's tenacity, flexibility and balanced capacity. Your muscles will be stronger. The Nike Free series' shoes have dynamic design and good structure of vamp. They also have three kinds of insoles which are flexible. In addition, Nike Company also offers another service.<br><br>It produces specific shoes for a specific person. So the customers of different levels can choose their own shoes. The company invites some prominent artists to design for the Nike Free series. These artists include Xiaohuang, Huang Wei, Fran?ois Tr�zin, Jin Ningning and QingtouThese five artists use the shoot and comic book to present the theme of "free".<br>They extend the innovative design concept of Nike Free. So we can see very lively and funny images because of their designs.<br><br>In 2004, the first Nike Free appeared in the world. Actually Nike Free shoes are very popular all the time since they appeared. The designer of Nike running shoes, Mark Miner expresses his views. When we design the shoes, we must pay attention every step. We hope that every step should be done well.<br>Nike Free series first bring in the dynamic design. The vamp is light and thin as the second skin. You can have the feeling of bared feet when you do some sports. In addition, we can not ignore the shoes' elasticity. This kind of shoes will conform to your feet's motions when you do exercises.<br><br>This kind of structural design is unique and good. We have to admit that the shoes' color, design and functionality are all unique and unmatched. The shoes are produced for natural motion and free running.<br>This kind of shoes brings comfort for our feet. In 2001, Nike Sport Research Lab collected the data when the sportsmen ran without shoes. Through the systematized test and study, they found that running with bared feet could keep the elasticity of our shanks and muscles of our feet.<br><br>Because of Nike Free, we reach this dream. German Sport University Cologne confirmed this fact in 2003 and 2004. Nike Free running shoes can expand the ankles' sphere of activities and increase the elasticity of our feet and ankles. Moreover, they are good for our muscles of feet.<br><br>According to different barefoot flexibility, the designers define Nike Free at different levels. 0.0 represents a completely barefoot running and 10.0 is equivalent to the flexibility of the standard running shoes of Nike Zoom Vomero. This time, we will bring three kinds of Nike Free running shoes for our customers.<br><br>The designers improve the designs of these shoes' midsoles and make the shoes beautiful. Moreover, the new seamless design provides a feeling nike air max of comfort and fitness. Among these new Nike Free series, Nike Free Run +3 and Nike Free 3.0 V4 will appear on the market in April 2012.<br>At the same time, in June we can find Nike Free 4.0 in the market.<br>Normal 0 7.8 � 0 2 false false false MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable mso-style-name:n |
| The viscoelastic property of a polymer is studied by dynamic mechanical analysis where a sinusoidal force (stress σ) is applied to a material and the resulting displacement (strain) is measured. For a perfectly elastic solid, the resulting strain and the stress will be perfectly in phase. For a purely viscous fluid, there will be a 90 degree phase lag of strain with respect to stress.<ref name="Meyers1999">{{cite book|last=Meyers|first=M.A.|coauthors=Chawla K.K.|title=Mechanical Behavior of Materials|publisher=Prentice-Hall|year=1999}}</ref> Viscoelastic polymers have the characteristics in between where some [[phase lag]] will occur during DMA tests.<ref name=Meyers1999/>
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| *Stress: <math> \sigma = \sigma_0 \sin(t\omega + \delta) \,</math> <ref name=Meyers1999/>
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| *Strain: <math> \varepsilon = \varepsilon_0 \sin(t\omega)</math>
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| where
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| :<math> \omega </math> is frequency of strain oscillation,
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| :<math>t</math> is time,
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| :<math> \delta </math> is phase lag between stress and strain.
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| The storage modulus measures the stored energy, representing the elastic portion, and the loss modulus measures the energy dissipated as heat, representing the viscous portion.<ref name=Meyers1999/> The tensile storage and loss moduli are defined as follows: | |
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| *Storage Modulus: <math> E' = \frac {\sigma_0} {\varepsilon_0} \cos \delta </math>
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| *Loss Modulus: <math> E'' = \frac {\sigma_0} {\varepsilon_0} \sin \delta </math>
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| *Phase Angle: <math> \delta = \arctan\frac {E''}{E'} </math>
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| Similarly we also define [[Shear modulus|shear storage]] and loss moduli, <math>G'</math> and <math>G''</math>.
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| Complex variables can be used to express the moduli <math>E^*</math> and <math>G^*</math> as follows:
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| :<math>E^* = E' + iE'' \,</math>
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| :<math>G^* = G' + iG'' \,</math>
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| where
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| :<math>{i}^2 = -1 \,</math>
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| ==Applications==
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| ===Measuring glass transition temperature===
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| [[Image:Temp Sweep Chem538.jpg|thumb|325px|Figure 2. A temperature sweep test on Polycarbonate. Storage Modulus (E’) and Loss Modulus (E’’) against temperature were plotted. Different initial static load and strain were used. The glass transition temperature of Polycarbonate was detected to be around 150 degree C.The Polycarbonate samples were made from the material purchased from Mcmaster-Carr, #8574k26]] One important application of DMA is measurement of the [[Glass_transition#Transition_temperature_Tg|glass transition temperature]] of polymers. Amorphous polymers have different glass transition temperatures, above which the material will have [[rubber]]y properties instead of glassy behavior and the stiffness of the material will drop dramatically with an increase in viscosity. At the glass transition, the storage modulus decreases dramatically and the loss modulus reaches a maximum. Temperature-sweeping DMA is often used to characterize the glass transition temperature of a material.
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| ===Polymer composition===
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| Varying the composition of monomers and [[cross-link|cross-linking]] can add or change the functionality of a polymer that can alter the results obtained from DMA. An example of such changes can be seen by blending ethylene-propylene-diene monomer (EPDM) with [[styrene-butadiene rubber]] (SBR) and different cross-linking or curing systems. Nair ''et al.'' abbreviate blends as E<sub>0</sub>S, E<sub>20</sub>S, etc., where E<sub>0</sub>S equals the weight percent of EPDM in the blend and S denotes sulfur as the curing agent.<ref name="Nair">{{cite journal|last=Nair|first=T.M.|coauthors=Kumaran, M.G.; Unnikrishnan, G.; Pillai, V.B.|year=2009|title=Dynamic Mechanical Analysis of Ethylene-Propylene-Diene Monomer Rubber and Styrene-Butadiene Rubber Blends|journal=Journal of Applied Polymer Science|volume=112|pages=72–81|doi = 10.1002/app.29367}}</ref>
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| Increasing the amount of SBR in the blend decreased the storage modulus due to [[intermolecular]] and [[intramolecular]] interactions that can alter the physical state of the polymer. Within the glassy region, EPDM shows the highest storage modulus due to stronger intermolecular interactions (SBR has more [[steric]] hindrance that makes it less crystalline). In the rubbery region, SBR shows the highest storage modulus resulting from its ability to resist intermolecular slippage.<ref name="Nair" />
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| When compared to sulfur, the higher storage modulus occurred for blends cured with dicumyl peroxide(DCP)because of the relative strengths of C-C and C-S bonds.
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| Incorporation of reinforcing fillers into the polymer blends also increases the storage modulus at an expense of limiting the loss tangent peak height.
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| DMA can also be used to effectively evaluate the miscibility of polymers. The E<sub>40</sub>S blend had a much broader transition with a shoulder instead of a steep drop-off in a storage modulus plot of varying blend ratios, indicating that there are areas that are not homogeneous.<ref name="Nair" />
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| ==Instrumentation==
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| [[Image:Schematic of DMA.png|thumb|Figure 3. General schematic of a DMA instrument.]]
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| The instrumentation of a DMA consists of a displacement sensor such as a linear variable differential transformer, which measures a change in voltage as a result of the instrument probe moving through a magnetic core, a temperature control system or furnace, a drive motor (a linear motor for probe loading which provides load for the applied force), a drive shaft support and guidance system to act as a guide for the force from the motor to the sample, and sample clamps in order to hold the sample being tested. Depending on what is being measured, samples will be prepared and handled differently. A general schematic of the primary components of a DMA instrument is shown in figure 3.<ref>{{cite web|url=http://www.mse.iastate.edu/research/research-groups/gom/laboratory-facilities/charaterization-lab/dma.html |title=DMA|accessdate=2010-02-02}}</ref> | |
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| ===Types of analyzers===
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| There are two main types of DMA analyzers used currently: forced resonance analyzers and free resonance analyzers. Free resonance analyzers measure the free oscillations of damping of the sample being tested by suspending and swinging the sample. A restriction to free resonance analyzers is that it is limited to rod or rectangular shaped samples, but samples that can be woven/braided are also applicable. Forced resonance analyzers are the more common type of analyzers available in instrumentation today. These types of analyzers force the sample to oscillate at a certain frequency and are reliable for performing a temperature sweep.
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| [[Image:Analyzers.png|thumb|left|Figure 4. Torsional versus Axial Motions.]]
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| Analyzers are made for both stress (force) and strain (displacement) control. In strain control, the probe is displaced and the resulting stress of the sample is measured by implementing a force balance transducer, which utilizes different shafts. The advantages of strain control include a better short time response for materials of low viscosity and experiments of stress relaxation are done with relative ease. In stress control, a set force is applied to the same and several other experimental conditions (temperature, frequency, or time) can be varied. Stress control is typically less expensive than strain control because only one shaft is needed, but this also makes it harder to use. Some advantages of stress control include the fact that the structure of the sample is less likely to be destroyed and longer relaxation times/ longer creep studies can be done with much more ease. Characterizing low viscous materials come at a disadvantage of short time responses that are limited by [[inertia]]. Stress and strain control analyzers give about the same results as long as characterization is within the linear region of the polymer in question. However, stress control lends a more realistic response because polymers have a tendency to resist a load.<ref name="book">{{cite book|last=Menard|first=Kevin P.|title=Dynamic Mechanical Analysis: A Practical Introduction|publisher=CRC Press|year=1999|chapter= 4 |isbn=0-8493-8688-8}}</ref>
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| Stress and strain can be applied via torsional or axial analyzers. Torsional analyzers are mainly used for liquids or melts but can also be implemented for some solid samples since the force is applied in a twisting motion. The instrument can do creep-recovery, stress-relaxation, and stress-strain experiments. Axial analyzers are used for solid or semisolid materials. It can do flexure, tensile, and compression testing (even shear and liquid specimens if desired). These analyzers can test higher modulus materials than torsional analyzers. The instrument can do [[thermomechanical analysis]] (TMA) studies in addition to the experiments that torsional analyzers can do. Figure 4 shows the general difference between the two applications of stress and strain.<ref name="book" />
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| Changing sample geometry and fixtures can make stress and strain analyzers virtually indifferent of one another except at the extreme ends of sample phases, i.e. really fluid or rigid materials. Common geometries and fixtures for axial analyzers include three-point and four-point bending, dual and single cantilever, parallel plate and variants, bulk, extension/tensile, and shear plates and sandwiches. Geometries and fixtures for torsional analyzers consist of parallel plates, cone-and-plate, couette, and torsional beam and braid. In order to utilize DMA to characterize materials, the fact that small dimensional changes can also lead to large inaccuracies in certain tests needs to be addressed. Inertia and shear heating can affect the results of either forced or free resonance analyzers, especially in fluid samples.<ref name="book" />
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| ===Test modes===
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| Two major kinds of test modes can be used to probe the viscoelastic properties of polymers: temperature sweep and frequency sweep tests. A third, less commonly studied test mode is dynamic stress-strain testing.
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| ====Temperature sweep====
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| A common test method involves measuring the complex modulus at low constant frequency while varying the sample temperature. A prominent peak in <math>\tan(\delta)</math> appears at the glass transition temperature of the polymer. Secondary transitions can also be observed, which can be attributed to the temperature-dependent activation of a wide variety of chain motions.<ref name = "Young">{{cite book|last=Young|first=R.J.|coauthors=P.A. Lovell|title=Introduction to Polymers|publisher=Nelson Thornes|year=1991|edition=2}}</ref> In [[semi-crystalline polymer]]s, separate transitions can be observed for the crystalline and amorphous sections. Similarly, multiple transitions are often found in polymer blends.
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| For instance, blends of [[polycarbonate]] and poly([[acrylonitrile-butadiene-styrene]]) were studied with the intention of developing a polycarbonate-based material without polycarbonate’s tendency towards [[brittle failure]]. Temperature-sweeping DMA of the blends showed two strong transitions coincident with the glass transition temperatures of PC and PABS, consistent with the finding that the two polymers were immiscible.<ref name=Mas>{{cite journal|last=J. Màs et al. |year=2002|title=Dynamic mechanical properties of polycarbonate and acrylonitrile-butadiene-styrene copolymer blends|doi=10.1002/app.10043|journal=Journal of Applied Polymer Science|volume=83|issue=7|pages=1507–1516}}</ref>
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| ====Frequency sweep====
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| [[Image:Freq Sweep Chem538.jpg|thumb|325px|Figure 5. A frequency sweep test on Polycarbonate under room temperature (25 °C). Storage Modulus (E’) and Loss Modulus (E’’) were plotted against frequency. The increase of frequency “freezes” the chain movements and a stiffer behavior was observed.]]
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| A sample can be held to a fixed temperature and can be tested at varying frequency. Peaks in <math>\tan(\delta)</math> and in E’’ with respect to frequency can be associated with the glass transition, which corresponds to the ability of chains to move past each other. Note that this implies that the glass transition is dependent on strain rate in addition to temperature. Secondary transitions may be observed as well.
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| The [[Maxwell material|Maxwell model]] provides a convenient, if not strictly accurate, description of viscoelastic materials. Applying a sinusoidal stress to a Maxwell model gives: <math> E'' = \frac{E \tau_0 \omega}{\tau_0^2 \omega^2 + 1} ,</math> where <math>\tau_0 = \eta/E</math> is the Maxwell relaxtion time. Thus, a peak in E’’ is observed at the frequency <math>1/\tau_0</math>.<ref name="Young" /> A real polymer may have several different relaxation times associated with different molecular motions.
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| ====Dynamic stress-strain studies====
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| By gradually increasing the amplitude of oscillations, one can perform a dynamic stress-strain measurement. The variation of storage and loss moduli with increasing stress can be used for materials characterization, and to determine the upper bound of the material’s linear stress-strain regime.<ref name="book" />
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| ====Combined sweep====
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| Because glass transitions and secondary transitions are seen in both frequency studies and temperature studies, there is interest in multidimensional studies, where temperature sweeps are conducted at a variety of frequencies or frequency sweeps are conducted at a variety of temperatures. This sort of study provides a rich characterization of the material, and can lend information about the nature of the molecular motion responsible for the transition.
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| For instance, studies of [[polystyrene]] (T<sub>g</sub> ~ 110 °C) have noted a secondary transition near room temperature. Temperature-frequency studies showed that the transition temperature is largely frequency-independent, suggesting that this transition results from a motion of a small number of atoms; it has been suggested that this is the result of the rotation of the [[phenyl]] group around the main chain.<ref name = "Young" />
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| ==See also==
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| * [[Maxwell material]]
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| * [[Standard Linear Solid Material]]
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| * [[Thermomechanical analysis]]
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| * [[Dielectric Thermal Analysis]]
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| * [[Time-temperature superposition]]
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| * [[Electroactive polymers]]
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Dynamic Mechanical Analysis}}
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| [[Category:Materials science]]
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| [[Category:Scientific techniques]]
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If you have a pair of Nike Free shoes, you can run freely and well.
In 2012, Nike Company produces new running shoes of Nike Free Run+3, Nike Free 4.0 and Nike Free 3.0 V4. The release of these shoes is held in an art garden of Sanlitun in Beijing. The technique of Nike Free can restore the natural motion of our feet and imitate the practice of bared feet.
It can improve our feet's tenacity, flexibility and balanced capacity. Your muscles will be stronger. The Nike Free series' shoes have dynamic design and good structure of vamp. They also have three kinds of insoles which are flexible. In addition, Nike Company also offers another service.
It produces specific shoes for a specific person. So the customers of different levels can choose their own shoes. The company invites some prominent artists to design for the Nike Free series. These artists include Xiaohuang, Huang Wei, Fran?ois Tr�zin, Jin Ningning and QingtouThese five artists use the shoot and comic book to present the theme of "free".
They extend the innovative design concept of Nike Free. So we can see very lively and funny images because of their designs.
In 2004, the first Nike Free appeared in the world. Actually Nike Free shoes are very popular all the time since they appeared. The designer of Nike running shoes, Mark Miner expresses his views. When we design the shoes, we must pay attention every step. We hope that every step should be done well.
Nike Free series first bring in the dynamic design. The vamp is light and thin as the second skin. You can have the feeling of bared feet when you do some sports. In addition, we can not ignore the shoes' elasticity. This kind of shoes will conform to your feet's motions when you do exercises.
This kind of structural design is unique and good. We have to admit that the shoes' color, design and functionality are all unique and unmatched. The shoes are produced for natural motion and free running.
This kind of shoes brings comfort for our feet. In 2001, Nike Sport Research Lab collected the data when the sportsmen ran without shoes. Through the systematized test and study, they found that running with bared feet could keep the elasticity of our shanks and muscles of our feet.
Because of Nike Free, we reach this dream. German Sport University Cologne confirmed this fact in 2003 and 2004. Nike Free running shoes can expand the ankles' sphere of activities and increase the elasticity of our feet and ankles. Moreover, they are good for our muscles of feet.
According to different barefoot flexibility, the designers define Nike Free at different levels. 0.0 represents a completely barefoot running and 10.0 is equivalent to the flexibility of the standard running shoes of Nike Zoom Vomero. This time, we will bring three kinds of Nike Free running shoes for our customers.
The designers improve the designs of these shoes' midsoles and make the shoes beautiful. Moreover, the new seamless design provides a feeling nike air max of comfort and fitness. Among these new Nike Free series, Nike Free Run +3 and Nike Free 3.0 V4 will appear on the market in April 2012.
At the same time, in June we can find Nike Free 4.0 in the market.
Normal 0 7.8 � 0 2 false false false MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable mso-style-name:n