Polydispersity, defined

The majority of microfluidic methods produce droplet using passive devices generating a uniform, evenly spaced, continuous stream of droplet, whose volume ranges from femtoliters to nanoliters. Their operational modes take advantage of the characteristics of the flow field to deform the interface and promote the natural growth of interfacial instabilities, avoiding in this way the necessity of any local external actuation. Droplet polydispersity, defined as the ratio between the standard deviation of the size distribution and the mean droplet size, can be as small as l%-3%. 

Polydispersity defines the spread of the components that make up a polymer. The narrowest distribution is, by definition, 1, and the closer a polymer is to this value, the more likely is it that MALDl can be used. Once the polydispersity approaches 2, it becomes difficult to obtain data and the samples should be fractionated using size exclusion chromatography and the fractions analyzed separately to obtain a correct representation of the overall makeup of the polymer. 

The values of a, width of the aggregation number distribution curve permit the calculation of the micelle polydispersity, defined as the ratio of the weight-average (N ) and number-average (Nn) micelle aggregation numbers, from NyN = 1 -h (a/N). For most of the entries in Table 3.1 the micelle polydispersity is low. This is because most of the measurements refer to surfactant concentrations close to the cmc, at which the micelles are generally small and spheroidal and, thus, of rather low poly-dispersity. For these systems it has been observed that a /N is close to unity. ... 

The major class of plate-like colloids is tliat of clay suspensions [21]. Many of tliese swell in water to give a stack of parallel, tliin sheets, stabilized by electrical charges. Natural clays tend to be quite polydisperse. The syntlietic clay laponite is comparatively well defined, consisting of discs of about 1 nm in tliickness and 25 nm in diameter. It has been used in a number of studies (e.g. [22]). 

Hven fractionated polymer samples are generally polydisperse, which means that the molecular weight determined from intrinsic viscosity experiments is an average value. The average obtained is the viscosity average as defined by Eqs. (1.20) and (2.40) as seen by the following argument ... 

For polydisperse systems the value of M obtained from the values of s° and D°-or, better yet, the value of the s/D ratio extrapolated to c = 0-is an average value. Different kinds of average are obtained, depending on the method used to define the average location of the boundary. The weight average is the type obtained in the usual analysis. 

A criterion for selecting a right pore size to separate a given polydisperse polymer is provided here. To quantify how much the MW distribution narrows for the initial fraction, an exponent a is introduced (2). The exponent is defined by [PDI(0)] = PDI(l), where PDI(O) and PDI(l) are the polydispersity indices of the original sample and the initial fraction, respectively. A smaller a denotes a better resolution. If a = 0, the separation would produce a perfectly monodisperse fraction. Figure 23.7 shows a plot of a as a function of 2RJd (2). Results... 

A potential drawback of all the routes discussed thus far is that there is little control over polydispersity and molecular weight of the resultant polymer. Ringopening metathesis polymerization (ROMP) is a living polymerization method and, in theory, affords materials with low polydispersities and predictable molecular weights. This methodology has been applied to the synthesis of polyacctylcne by Feast [23], and has recently been exploited in the synthesis of PPV. Bicyclic monomer 12 [24] and cyclophane 13 [25) afford well-defined precursor polymers which may be converted into PPV 1 by thermal elimination as described in Scheme 1-4. 

It should be stressed that the observed critical strain-rate for bond fracture (sf) in the case of a polydisperse fraction refers to the longest chain present in the sample. This quantity is significantly different from the critical strain-rate (r ) defined with respect to an average molecular mass whose value could be determined only after careful consideration of the degradation kinetics. 

The critical point (Ij of the two-phase region encountered at reduced temperatures is called an upper critical solution temperature (UCST), and that of the two-phase region found at elevated temperatures is called, perversely, a lower critical solution temperature (LCST). Figure 2 is drawn assuming that the polymer in solution is monodisperse. However, if the polymer in solution is polydisperse, generally similar, but more vaguely defined, regions of phase separation occur. These are known as "cloud-point" curves. The term "cloud point" results from the visual observation of phase separation - a cloudiness in the mixture. 

The growing polymer chains have the most probable distribution defined by Equation (13.26). Typically, is large enough that PD 2 for the growing chains. It remains 2 when termination occurs by disproportionation. Example 13.5 shows that the polydispersity drops to 1.5 for termination by pure combination. The addition rules of Section 13.2.2 can be applied to determine 1.5 < PD < 2 for mixed-mode terminations, but disproportionation is the predominant form for commercial polymers. 

In order to enhance the understanding of the properties in polymers, iterative pathways have been chosen for the synthesis of structurally perfect molecules. Data obtained from the analysis of precisely defined oligomers and polymers may relate chain length and conformation to physical, electronic and optical properties. Statistical polymerization processes are not suitable as they yield polydisperse material. 

Application in the Field of Scattering. Let us consider two important distribution functions, hc (x) and lu. (x). These functions shall describe the thicknesses of crystalline layers and the distances (long periods) between them, respectively. In this case we take into account polydispersity of the crystalline layers, if (at least) the two parameters dc and ac/dc are determined which are defined as the average thickness of the crystalline layers,... 

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