Nip, nips

To attain a transverse field profile that is confined within the defect, the profile must exponentially increase for p < pdef, and exponentially decrease for p > pdef. This requirement determines which index-interfaces (lowhigh or highlow) should be positioned at zeros of the field and which at the extrema of the field. The constraints on the index profile are similar to the Cartesian case and differ for the TE and TM polarizations. For the TE polarization, the interfaces for decreasing (increasing) field should be at the zeros (extrema) of If, if nip ) > n(p 1) at the interface and at the extrema (zeros) of Hz if nip ) < nip 1) at the interface. For the TM polarization, the interfaces for decreasing (increasing) field should be at the extrema (zeros) of E, if n(p ) > n(p+) at the interface and at the zeros (extrema) of E, if n(p ) < nip 1) at the interface. The interfaces of the defect must be located at zeros of II, for TE and of E, for TM. 

Since the vacancy in the nip orbital behaves, in this respect, like a single electron, the states arising are the same as those from nlp) n 2p), since we can ignore electrons in filled orbitals. Equation (7.77), dropping the g and u subscripts for a heteronuclear diatomic molecule, gives... 

Sheet can be produced by melt extmsion, but in this case a three-roll stack of quenching roUs is generally used (Fig. 2). More than three roUs may be used where necessary. The roUs may be mounted vertically or horizontally. The web is extmded through a slot die in a thickness close to the desired final thickness. The die is in very close proximity to the first chill roU or chill-roll nip. The web may be cast horizontally directly onto the upper chill roU of the stack as shown (Fig. 2), or it may be extmded into the first nip directly. The roUs quench the sheet and provide the surface polish desired. In some applications, matte or embossed roUs maybe used to impart special surface characteristics for certain functions. Where the utmost in optical (glazing) quality is desired the trend has been to mount the roU stack horizontally. The hot melt is then extmded vertically down into the first nip. This avoids problems associated with sag of a horizontal hot melt no matter how short the distance between die and quench. 

The film tube is collapsed within a V-shaped frame of rollers and is nipped at the end of the frame to trap the air within the bubble. The nip roUs also draw the film away from the die. The draw rate is controlled to balance the physical properties with the transverse properties achieved by the blow draw ratio. The tube may be wound as such or may be sHt and wound as a single-film layer onto one or more roUs. The tube may also be direcdy processed into bags. The blown film method is used principally to produce polyethylene film. It has occasionally been used for polypropylene, poly(ethylene terephthalate), vinyls, nylon, and other polymers. 

In extmsion coating a polymer is extmded from a slot die into the nip of two roUs where it is bonded to a substrate under pressure (Fig. 6). A corona discharge may be appUed to the substrate just prior to the nip to enhance adhesion. Polyethylene or ionomer are the most common resins used in extmsion coatings. They provide improved moisture barrier (on paper), or sealabUity (on foU, polypropylene, or polyester). When a second substrate is introduced to the nip, laminated stmctures may be produced. 

Ko//M //s. When dispersion is requited ia exceedingly viscous materials, the large surface area and small mixing volume of roU mills allow maximum shear to be maintained as the thin layer of material passiag through the nip is continuously cooled. The roUs rotate at different speeds and temperatures to generate the shear force with preferential adhesion to the warmer roU. 

Nonstabilized foams are referred to as froths froth-bonded fabrics are similar in properties to some saturation-bonded nonwovens. Typical foams used as nonwoven binder solutions have a consistency similar to shaving cream. AppHcation methods include knife-edge layering onto a horizontal web surface followed by vacuum penetration, and saturation and penetration of a vertical web surface using a horizontal-nip pad. Drying and curing is carried out in ovens, dmm dryers, or steam cans. 

Smooth surfaces are normally estabflshed by calendering, a process which subjects the fabric at the nip point(s) of two or more roUs to the influence of controlled time, temperature, and pressure. When calendering is used as a thermal-bonding process, the roUs are of the same dimension and composition and are independently driven. However, when calendering is used as a fabric finishing operation, the roUs are frequently of different dimensions and composition and are not always independently driven. 

Processes. The most common method for the appHcation of chemicals to the surface of a paper web is by a size press. In the size press, dry paper, which usually is sized to prevent excess water and chemical penetration, is passed through a flooded nip or pond, and a solution or dispersion of the functional chemical contacts both sides of the paper. Excess Hquid is squeezed out in a press and the paper is redried. 

At high speeds, the pond of the flooded nip size press becomes turbulent. RoU maintenance is a problem with the gate-roU size press. To avoid these problems, the blade/rod metering size press was developed. Short-dweU coater heads are used to apply a precisely controUed quantity of chemicals to the size press roUs. This quantity is controUed with either a metering blade or a metering rod. Blade or rod metering eliminates the pond, and does not increase the number of roUs required for surface chemical appHcation. 

Phosphides. Compounds of phosphoms containing the more electropositive elements are generally called phosphides. A large number of binary phosphides as well as many ternary mixed-metal phosphides, metal phosphide nitrides, etc, are known. Some binary phosphides, such as those of nickel, exhibit a variety of stoichiometries (Ni P, Ni P2, Nq2P5, Ni2P, Ni P, NiP, NiP2, NiP ), whereas others, such as aluminum, form only one (AlP). Metalloids such as B and Si also form phosphides. 

A web of molten plastic is pulled from the die into the nip between the top and middle roUs. At the nip, there is a very small rolling bank of melt. Pressure between the roUs is adjusted to produce sheet of the proper thickness and surface appearance. The necessary amount of pressure depends on the viscosity. For a given width, thickness depends on the balance between extmder output rate and the take-off rate of the pull roUs. A change in either the extmder screw speed or the puU-roU speed affects thickness. A constant thickness across the sheet requires a constant thickness of melt from the die. The die is equipped with bolts for adjusting the die-gap opening and with an adjustable choker bar or dam located inside the die a few centimeters behind the die opening. The choker bar restricts flow in the center of the die, helping to maintain a uniform flow rate across the entire die width. 

Drawdown from the die to nip is typically ca 10%. Sheet extmsion requires that the resin be of high melt viscosity to prevent excessive sag of the melt between the die and the nip. The melt should reach the nip before touching any other part of the middle roU to prevent uncontrolled cooling of the resin. The appearance of the lower surface of the sheet is deterrnined by the middle roU, ie, its poHsh, surface temperature, and freedom from condensed materials. The upper surface is cooled by air and has a more glossy appearance. Neither the top roU nor the bottom roU greatly affect the appearance of the top surface of the sheet. Edges of the sheet are trimmed. 

In contrast to most extmsion processes, extmsion coating involves a hot melt, ca 340°C. The thin web cools rapidly between the die and nip even at high linear rates. Both mechanical and chemical bonding to substrates are involved. Mechanical locking of resin around fibers contributes to the resin s adhesion to paper. Some oxidation of the melt takes place in the air gap, thereby providing sites for chemical bonding to aluminum foil. Excessive oxidation causes poor heat-sealing characteristics. 

Additional complications can occur if the mode of deformation of the material in the process differs from that of the measurement method. Most fluid rheology measurements are made under shear. If the material is extended, broken into droplets, or drawn into filaments, the extensional viscosity may be a more appropriate quantity for correlation with performance. This is the case in the parting nip of a roUer in which filamenting paint can cause roUer spatter if the extensional viscosity exceeds certain limits (109). In a number of cases shear stress is the key factor rather than shear rate, and controlled stress measurements are necessary. 

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