Molecular mass Viscosity

Liquid Phase Solvent Average Molecular Mass Viscosity Tmin, °c Tmaxi °c... 

The numerous cellulose derivatives commercially available, displaying varying second order transition, molecular mass, viscosity, lyophilicity, thermotropic properties, have considerable potential. Significant advances have been made in the collection of fundamental data, but the interpretation of this information is somewhat more difficult than for synthetic polymers, mostly because of the heterogeneity of the materials, which exhibit a broad molecular mass distribution and an uneven substitution. 

Polymer Source and trade name Molecular mass Viscosity money ML (1+4) 100° C... 

An average molecular mass (viscosity average) An average molecular mass (number average) Molecular dimensions and an average molecular mass (weight average) Molecular mass distribution... 

Compared with atactic polypropylene it has a lower softening point (less than 100°C compared with 154°C when assessed by ball and ring methods), has better resistance to subzero temperatures and is completely soluble in aliphatic hydrocarbons. The molecular mass of atactic polybut-l-ene is about twice that of an atactic polypropylene of similar melt viscosity. 

ASTM, Standard Test Method for Estimation of Molecular Weight (Relative Molecular Mass) of Petroleum Oils from Viscosity Measurements, ASTM Standard D-2502-92, 1992. 

Fig. 2 a, b. Dependence of the maximum Newton viscosity (t/0) (a) and swelling ratio of the extrudate (D) (b) on the molecular mass of cis-1,4-polyisoprene, unfilled and filled to 33% by mass. Filler 1 — not 2 — CaC03 with specific surface areas 2-3 m2/g 3 — ash PM —15 with specific surface areas 12-18m2/g 4 — ash PM-100 with specific surface areas 90-100 m2/g... 

Note that, apart from the filler particle shape and size, the molecular mass of the base polymer may also have a marked effect on the viscosity of molten composites [182,183]. The higher the MM of the matrix the less apparent are the variations of relative viscosity with varying filler content. In Fig. 2, borrowed from [183], one can see that the effect of the matrix MM on the viscosity of filled systems decreases with the increasing filler activity. In the quoted reference it has also been shown that the lg r 0 — lg (MM)W relationships for filled and unfilled systems may intersect. The more branches the polymer has, the stronger is the filler effect on its viscosity. The data for filled high- (HDPE) and low-density polyethylene (LDPE) [164,182] may serve as an example the decrease of the molecular mass of LDPE causes a more rapid increase of the relative viscosity of filled systems than in case of HDPE. When the values (MM)W and (MM)W (MM) 1 are close, the increased degree of branching results in increase of the relative viscosity of filled system [184]. 

This equation appears to have a number of names, of which the Mark-Houwink equation is the most widely used. In order to use it, the constants K and a must be known. They are independent of the value of M in most cases but they vary with solvent, polymer, and temperature of the system. They are also influenced by the detailed distribution of molecular masses, so that in principle the polydispersity of the unknown polymer should be the same as that of the specimens employed in the calibration step that was used to obtain the Mark-Houwink constants originally. In practice this point is rarely observed polydispersities are rarely evaluated for polymers assigned values of relative molar mass on the basis of viscosity measurements. Representative values of K and a are given in Table 6.4, from which it will be seen that values of K vary widely, while a usually falls in the range 0.6-0.8 in good solvents at the 0 temperature, a = 0.5. 

When bounding walls exist, the particles confined within them not only collide with each other, but also collide with the walls. With the decrease of wall spacing, the frequency of particle-particle collisions will decrease, while the particle-wall collision frequency will increase. This can be demonstrated by calculation of collisions of particles in two parallel plates with the DSMC method. In Fig. 5 the result of such a simulation is shown. In the simulation [18], 2,000 representative nitrogen gas molecules with 50 cells were employed. Other parameters used here were viscosity /r= 1.656 X 10 Pa-s, molecular mass m =4.65 X 10 kg, and the ambient temperature 7 ref=273 K. Instead of the hard-sphere (HS) model, the variable hard-sphere (VHS) model was adopted in the simulation, which gives a better prediction of the viscosity-temperature dependence than the HS model. For the VHS model, the mean free path becomes ... 

Mature human albumin consists of one polypeptide chain of 585 amino acids and contains 17 disulfide bonds. By the use of proteases, albumin can be subdivided into three domains, which have different functions. Albumin has an ellipsoidal shape, which means that it does not increase the viscosity of the plasma as much as an elongated molecule such as fibrinogen does. Because of its relatively low molecular mass (about 69 kDa) and high concentration, albumin is thought to be responsible for 75-80% of the osmotic pressure of human plasma. Electrophoretic smdies have shown that the plasma of certain humans lacks albumin. These subjects are said to exhibit analbuminemia. One cause of this condition is a mutation that affects spUcing. Subjects with analbuminemia show only moderate edema, despite the fact that albumin is the major determinant of plasma osmotic pressure. It is thought that the amounts of the other plasma proteins increase and compensate for the lack of albumin. 

Sam- ple Nr Method for obtaining Polysaccharide yield g/L culture medium, g Polyuronides DE, PUAC, % % Molecular mass Intrinsic viscosity dlxg" Huggins constant Kh... 

The data on the molecular mass and on the intrinsic viscosity confirmed the expectation that the fraction, precipitated under freezing, had a higher molecular mass (Table 1). 

Abbreviations PUAC, polyuronic acid content DE, concentration ri, specific viscosity Mj, molecular mass... 

Fig. 9. Kinematic viscosity v = r /p (r viscosity, p density) divided by S2/M (S2 = mean square radius of gyration, M molecular mass) as a function of M for polyethylene melts at the same monomeric friction coefficient. (Reprinted with permission from [48]. Copyright 1987 American Chemical Society, Washington)...

This is done in Fig. 15 where the viscosity is shown as a function of molecular mass. The open circles represent the predictions of the NSE result, whereas the filled circles represent the viscosity measurement. Both data sets are in excellent agreement and demonstrate the consistency of evaluation. 

In addition to the Rouse model, the Hess theory contains two further parameters the critical monomer number Nc and the relative strength of the entanglement friction A (0)/ . Furthermore, the change in the monomeric friction coefficient with molecular mass has to be taken into account. Using results for (M) from viscosity data [47], Fig. 16 displays the results of the data fitting, varying only the two model parameters Nc and A (0)/ for the samples with the molecular masses Mw = 3600 and Mw = 6500 g/mol. 

Fig. 15. Comparison of the viscosities either directly measured or calculated from the spin-echo results for polyethylene melts at 509 K as a function of molecular mass ( experimental result o viscosities calculated on the basis of mode analysis). (Reprinted with permission from [52]. Copyright 1993 The American Physical Society, Maryland)...

On the other hand, it was found that the microscopic parameter pH(c) exhibits close similarities to the macroscopic viscosity r (c)/r s of a low molecular mass (M 7.400 g/mol) PDMS/d-chlorobenzene system at 373 K. For that low molar mass the terminal Zimm time tz [see Eq. (80)] is comparable to the time scale of the NSE experiment. Thus, the macroscopic viscosity can relax towards... 

Performing what is known as post-condensation. Most step polymerisations are exothermic and, consequently, the equilibrium constant K decreases with increasing temperature. Hence, one way to increase the molecular mass would be to decrease the polymerisation temperature, but kinetics prohibits using a too low temperature as it will lead to an excessively long residence time in the reactor and/or too high viscosities. Thus, in order to reach very high molecular... 

Schulze and Crouch [7] observed that the viscosity of the soluble fraction of copolymers from butadiene and styrene decreased sharply with the conversion after an initial increase up to the point of gelation. This decrease could not be solely attributed to a selective incorporation of higher molecular mass fractions in the gel, thus leaving fractions of low molecular mass in solution. Cragg and Manson [8] reported a similar relationship between the intrinsic viscosity and the fraction of the crosslinking DVB in the ECP with styrene. Within the concentration range up to 0.1 mass % of DVB no gel was formed. Therefore, a selective removal of species with a high molecular mass could not have taken place to explain the decrease in the intrinsic viscosity observed after its increase at lower concentrations of DVB. 

A packed column, 1.2 m in diameter and 9 m tall, is packed with 25 mm Raschig rings, and used for the vacuum distillation of a mixture of isomers of molecular mass 155 kg/kmol. The mean temperature is 373 K, the pressure at the top of the column is maintained at 0.13 kN/m2 and the still pressure is 1.3-3.3 kN/m2. Obtain an expression for the pressure drop on the assumption that this is not appreciably affected by the liquid flow and may be calculated using a modified form of Carman s equation. Show that, over the range of operating pressures used, the pressure drop is approximately directly proportional to the mass rate of flow rate of vapour, and calculate the pressure drop at a vapour rate of 0.125 kg/m2. The specific surface of packing, S = 190 m2/m3, the mean voidage of bed, e = 0.71, the viscosity of vapour, // = 0.018 mN s/m2 and the molecular volume = 22.4 m3/kmol. 

Keywords Thermo-mechanical destruction, polypropylene, molecular mass, effective viscosity. 

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