Draw resonance

Draw resonance occurs in processes where the extrudate is exposed to a free surface stretching flow, such as blown film extrusion, fiber spinning, and blow molding. It manifests itself in a regular cyclic variation of the dimensions of the extrudate. An extensive review [169] and an analysis [170] of draw resonance were done by Petrie and Denn. Draw resonance occurs above a certain critical draw ratio while the polymer is still in the molten state when it is taken up and rapidly quenched after take-up. 

Draw resonance will occur when the resistance to extensional deformation decreases as the stress level increases. The total amount of mass between die and take-up may vary with time because the take-up velocity is constant but not necessarily the extrudate dimensions. If the extrudate dimensions reduce just before the take-up, the extrudate dimensions above it have to increase. As the larger extrudate section is taken up, a thin extrudate section can form above it this can go on and on. Thus, a cyclic variation of the extrudate dimensions can occur. Draw resonance does not occur when the extrudate is solidified at the point of take-up because the extrudate dimensions at the take-up are then fixed [171, 172]. Isothermal draw resonance is found to be independent of the flow rate. The critical draw ratio for almost-Newtonian fluids such as nylon, polyester, polysiloxane, etc., is approximately 20. The critical draw ratio for strongly non-Newtonian fluids such as polyethylene, polypropylene, polystyrene, etc., can be as low as 3 [173]. The amplitude of the dimensional variation increases with draw ratio and drawdown length. 

Various workers have performed theoretical studies of the draw resonance problem by linear stability analysis. Pearson and Shah [174,175] studied inelastic fluids and predicted a critical draw ratio of 20.2 for Newtonian fluids. Fisher and Denn [176] confirmed the critical draw ratio for Newtonian fluids. Using a linearized stability 

The exposure time Xf of the wiped film as it travels with the barrel surface from the flight clearance to the melt pool is  

The total volumetric flow rate of the wiped film is  

There are two unique aspects to the water-quenching of polypropylene. As with other thermoplastic melts, this material exhibits draw resonance under certain spinning conditions. Polypropylene apparently is more susceptible to this phenomenon than many other materials. Under certain conditions, the filament will be uniform all along its length. If the take-up speed is increased, a critical value of speed will be reached when the filament diameter begins to oscillate in a regular manner. The amplitude of diameter oscillation can reach 10-50% of the nominal diameter of the filament. The instability seems to be related to a critical value of the ratio Ft/ Fe, where Fj is take-up velocity and Fe is extrusion velocity. The critical ratio is affected by resin properties, extrusion temperature, filament nominal diameter, distance between spinneret and bath, and perhaps other process parameters. 

When polypropylene is water-quenched under eertain conditions, a difference in crystalline order is obtained. In air-quench systems, yarns with a crystallinity of around 55% are obtained. The crystals are usually distributed throughout the yarn as lamellae and are normally in the monoclinic a-form. In the rapidly cooling water-quench process, a less-ordered smectic or paracrystalline structure is produced with a morphology that is basically fibrillar. Under certain drawing conditions, these smectic structures lead to high-strength fibers. 

The orientation of the spun monofilaments and, consequently, the draw ratio necessary for producing a satisfactory product depend on the stretch rate during spinning and quenching, just as they do in the air-quench process. The larger the stretch rate, the higher the spin-line stress, the higher the orientation, and the lower the required draw ratio. 

After the filaments leave the quench tank, they must be wiped or blown free of water in preparation for hot-drawing. Wet sections of the yarn will not be heated to the same temperature as the dry sections. The process for drawing monofilaments is very similar to ST. Roll stands and hot ovens, baths, or plates are used for the filaments. The yarns are usually annealed on heated rolls or in an air oven. A two-stage yarn may be used, with a total draw ratio commonly around 6 1. A finish must be applied to the filaments for lubrication and static control. The filaments are wound individually on tubes or flanged bobbins. 

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Display and examine electrostatic potential maps for ethyl cation, 2-propyl cation and 2-methyl-2-propyl cation. Which cation shows the greatest localization of positive charge If you find that the methyl groups delocalize the positive charge, where does the charge go Write resonance contributors for the three cations to rationalize your conclusion. (Note You may need to draw resonance contributors that contain a CC double bond and are missing a CH bond see also Chapter 7, Problem 8.)... 

Compare energies for the two alternative conjugate acids of methyl acetate (protonated methyl acetate and methoxy protonated methyl acetate) and dimethylacetamide (N-protonated dimethylacetamide and 0-protonated dimethylacetamide). Which acid in each pair is more stable Draw resonance contributors for the more stable conjugate acid for each system. 

Onto which atoms (carbon, nitrogen or both) is the unpaired electron in tricyanomethyl radical delocalized Rationalize your result by drawing resonance contributors. 

Draw resonance structures for the possible radicals resulting from hydrogen atom abstraction from toluene. Which would you anticipate to be the most stable Why Compare energies for the different radicals (radical A, radical B,. ..). Is the lowest-energy radical that which you anticipated Are any of the alternatives significantly better than any of the others Explain your reasoning. 

First, try to draw resonance contributors for both ground state and triplet anthrone. Then display a spin density surface for the triplet state of anthrone. (Note that the spin density surface shows the location of both unpaired electrons, one of which may be in a 7t orbital and one of which may be in a o orbital.) Where are the two unpaired electrons Are they localized or delocalized Given that spin delocalization generally leads to stabilization, would you expect the triplet state of anthrone to be stable ... 

Thomson Click Organic Interactive to use an online palette to practice drawing resonance forms. 

Look back at the resonance forms of the acetate ion and the acetone anion shown in the previous section. The pattern seen there is a common one that leads to a useful technique for drawing resonance forms. In general, any three-atom grouping with a p orbital on each atom has two resonance forms. 

Draw resonance structures for the benzyl radical, C6H5CH2-, the intermediate produced in the NBS bromination reaction of toluene (Problem 10.27). 

Problem 16.14 Draw resonance structures for the intermediates from reaction of an electrophile at the ortho, meta, and para positions of nitrobenzene. Which intermediates are most stable ... 

The nitroso group, — N = Op is one of the few nonhalogens that is an ortho- and para-directing deactivator. Explain by drawing resonance structures of the carbocation intermediates in ortho, mela, and para electrophilic reaction on nitrosobenzene, C<3Hs N = 0. 

At what position, and on what ring, would you expect bromination of benz-anilide to occur Explain by drawing resonance structures of the intennediates. 

Draw resonance structures of the intermediate carbocations in the bromillation of naphthalene, and account for the fact that naphthalene undergoes electrophilic substitution at Cl rather than C2. 

You knowr the mechanism of HBr addition to alkenes, and you know the effects of various substituent groups on aromatic substitution. Use this knowledge to predict which of the following two alkenes reacts faster with HBr. Explain your answer by drawing resonance structures of the carbocation intermediates. 

Phenols (ArOH) are relatively acidic, and the presence of a substituent group on the aromatic ring has a large effect. The pKa of unsubstituted phenol, for example, is 9.89, while that of p-nitrophenol is 7.15, Draw resonance structures of the corresponding phenoxide anions and explain the data. 

Problem 24.24 Indole reacts with electrophiles at C3 rather than at C2. Draw resonance forms of the intermediate cations resulting from reaction at C2 and C3, and explain the observed results. 

Account for the fact that p-nitroaniline (pKa = 1.0) is less basic than m-nitroaniline (pKa = 2.5) by a factor of 30. Draw resonance structures to support your argument. (The p/Ca values refer to the corresponding ammonium ions.)... 

Draw resonance forms for the purple anion obtained by reaction of ninhydrin with an n-amino acid (Problem 26.53). 

Draw resonance structures for the trimethylenemethane anion C(CH,) 2 in which a central carbon atom is attached to thi ee CH, groups (CH, groups are referred to as methylene). 

Draw resonance structures of cyanobenzene (C H5CN) that show how it functions as a meta-directing substituent. 

Never draw a carbon atom with more than fonr bonds. This is a big no-no. Carbon atoms only have fonr orbitals therefore, carbon atoms can form only fonr bonds (bonds are formed when orbitals of one atom overlap with orbitals of another atom). This is true of all second-row elements, and we discuss this in more detail in the chapter on drawing resonance structures. 

In this chapter, you will learn the tools that you need to draw resonance structures with proficiency. I cannot adequately stress the importance of this skill. Resonance is the one topic that permeates the entire subject matter from start to finish. It finds its way into every chapter, into every reaction, and into your nightmares if you do not master the rules of resonance. You cannot get an A in this class without mastering resonance. So what is resonance And why do we need it ... 

CURVED ARROWS THE TOOLS FOR DRAWING RESONANCE STRUCTURES ... 

Now we know what curved arrows are, but how do we know when to push them and where to push them First, we need to learn where we cannot push arrows. There are two important rules that you should never violate when pushing arrows. They are the two commandments of drawing resonance structures ... 

Never break a single bond when drawing resonance structures. By definition, resonance stractures must have aU the same atoms connected in the same order. 

From now on, we will refer to the second commandment as the octet rule. But be careful—for purposes of drawing resonance structures, it is only a violation if we exceed an octet for a second-row element. However, there is no problem at all with a second-row element having fewer than an octet of electrons. For example ... 

EXERCISE 2.1 For the componnd below, look at the arrow drawn on the strnc-ture and determine whether it violates either of the two commandments for drawing resonance structnres ... 

This is why we need resonance—it shows us where there are regions of high and low electron density. If we draw resonance structures without formal charges, then what is the point in drawing the resonance structures at all ... 

Now we have all the tools we need. We know why we need resonance structures and what they represent. We know what curved arrows represent. We know how to recognize bad arrows that violate the two commandments. We know how to draw arrows that get you from one structure to another, and we know how to draw formal charges. We are now ready for the final challenge using curved arrows to draw resonance structures. 

Now we are ready to get some practice drawing resonance structures. 

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