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 Strictly speaking the viscosity average molecular weight will be the same  the molecular weight distibution not necessarily. For this you have to make GPC. This can be important if you try to compare PMMA samples of different origin, prepared by various techniques, with different tacticity etc. If, however, you compare samples prepared by th same polymerization technique and you want to study the effect of polmyerization parameters on the average molecular wight, you can rely on this simple technique.
 I definatelly agree with Dr Bahnegyi. Will be sure about the average molecular weight. You will not be sure about the despersion of the different polymer chain leghts (molecular weights).
 Yes it should! however they can have some slight differences in MWD.
Do you tell about solution viscosity or molten viscosity?  What do you mean by the viscosity of PMMA? Do you mean the intrinsic viscosity, same solvent/temperature? In this case, I agree with previous answers.
 Intrinsic viscosity of the polymer related to molecuar weight by MarkHouwink rule. Molecular weight distribution also affect the viscosity. Polymer with broad molecuar weight distribution shows less viscosity.
 You can confirm big differences in MW by doing some DSC on your samples. The smaller the MW, the lower the Tm. Try the average of at least three runs in order to be sure of the results.
 Theoretically, it should be the same. But in practice its seldom observed. Number or weight average molecular weight can be more realistic comparison.
Some one suggested MarkHowinkSakurada relation.. but it has two parameters K and a which are dependent on the type of solvent & its interaction with the polymer.  You should check the viscosity average molecular weight and number average molecular weight by GPC. This will confirm the relativity of viscosity and molecular weight.
 Always viscosity is related to MW.
 Assuming the wt% of the solute is the same throughout the different samples, yes. The viscosity as a general rule should be proportional to the MW.
 Melt viscosity is strongly related to MW, particularly when it is above the "entanglement MW" of the polymer. Above this critical MW, viscosity is often proportional to the power of 3.4 of its MW
 All previous answers are substantially correct and point out that while qualitatively viscosity increases with molecular weight the quantitative aspects can be affacted by molecular weight distribution even if the numebr average Mn is the same.Indeed the mol weight determined by the MarkHowink eq is much closer to the weight averge than to the number average , this implies that by incresing polydisopersity the intrinsic viscosity increases even if Mn remains constant. I like to add that viscosity is related to the hydrodynamic volume and incresaes with it , then better interacting solvents gives an increase of viscosity. The hydrodynamic volume depends also on branching and then different branching degree correspond to different viscosity even if Mn is the same.
 Please refer my papers
 An important parameter seems to be omited.
Difference of molecular weights, to what extent?
Huge difference of MW can easily be detected on trivial instruments.
From what read in this topic, we just dont have any idea of that MW difference.
Considering this, I'd vote for Rajeev Mehta reply because GPC/SEC technics permit a wider range of divers MW. Viscosity on a basic mechanical viscometer, using highly dilute solutions to build a graph and regress to the origin?
Extrapolation has it limits! Yes, the higher the MW is, the higher the viscosity in a given solvent will be as long as it is soluble.
In short, are you using the right laboratory automated instrument?
I was only curious.
Pierre.  Distribution of molecular weight can be analysed very easily by plotting viscosity data at different shear rate.If you would have CONE Plate rheometer just apply different shear rate to your sample and findout Viscosity at these different shear rate.Plot viscosity Vs shear rate graph,if viscosity will constsnt for different shear rate then We can say that Weight average and number average molecular weight in your sample are equal if there is no constant values of viscosity for different shear rate then your sample will be polydisperse. For more detail read Book by BIlmeyer naming polymer science
 yes,it is
 In general viscosity is related to molecular weight. It increases with increase in mol. weight. Polymers melts  melt flow index (as PMMA), however polymer solutions by traditional cheap methodsOstwald viscometer could be used. Latter method, gives value for viscosity average molecular weight different from Number avg and wt. average mol. wt (Mv>Mw>Mv). You can determine all the three and PDI by GPC technique.
Your sample showed same viscosity suggest may be same mol. wt. but also you need to check MWD through GPC.  You are talking about a polymer. There are many forms of molecular weight expression; number average Mn,viscosity average Mv, weight average Mw, zaverage Mz. Therefore, same viscosity does not imply same molecular weight. For example, if you have a sample containing a mixture of high and low molecular weight polymers, and another sample having a monodisperse MW distribution. The two samples may have the same viscosity but their molecular weights are unlikely to be the same.
So, the answer is: we can not conclude the molecular weights to be same based on viscosity test results. 
Usually intrinsic viscosity is more related with molecular weight. we can calculate viscosity average molecular weight from IV. BUT intrinsic viscosity of a polymer is very different from "viscosity".

Here is the detail information of relation between viscosity and molecular weight
http://www.ias.ac.in/initiat/sci_ed/resources/chemistry/Viscosity.pdf

The intrinsic viscosity is a reflection of the size of a polymer molecule in solution. It is measured by precisely measuring the effect a polymer sample has on the viscosity of a solvent. The exact definition is the zero concentration value of 1/c * ln (viscosity of polymer solution/viscosity of the solvent). It is most accurately and easily determined using a forced flow relative viscometer, and very dilute (ca 0.1% wt/vol or less) solutions of the polymer of interest. The units are usually dl/g (deciliters per gram).

so, how can the molecular weight of a polymer for example poly(ethylene oxide, Mv= 400,000) be calculated from its viscosity average molecular weight?

The viscosity average molecular weight can be calculated using the Mark Houinck relationship.
Needless to say, since typical polymers are mixtures of molecules of different sizes (from different degrees of polymerization), there are a range of sizes, and this range can be quantitatively described using the distribution concept, typically plotted as N vs M, where N is the relative number of molecules and M is the molecular mass.
The value obtained is an average for the distribution of sizes and molecular weights in the particular sample. If one assumes a particular distribution shape for a sample, the various moments of the distribution function can be calculated. (The first moment is called the number average molecular weight, the second moment is called the weight average molecular weight, the third moment is called the Z average molecular weight, and the fourth moment is called the Z+1, and so on.)
The various moments of the distribution generally correlate with mechanical properties of different time scales.
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